Adorno's despair derives precisely from the fact that nothing more than instrumental reason is retained when we think through "the basic process of conscious life" radically enough in the categories provided by the philosophy of consciousness. Habermas, The Theory of Communicative Action, Vol 1, p.396

In the atomistic perspective of much of modern thought, the subject stands over against a world of objects to which it has two basic relations: representation and action. Accordingly, the type of rationality associated with this model is the "cognitive-instru- mental" rationality of a subject capable of gaining knowledge about a contingent environment and putting it to effective use in intelligently adapting to and manipulating that environment. By stressing the fact that the goal-directed actions of different individuals are socially coordinated, Habermas shifts our attention to the broader context of individual purposive actions, to the structures of social interaction in which teleological actions are located. McCarthy, Translator’s Introduction in The Theory of Communicative Action, p.ix

His [Weber’s] hierarchy of concepts of action is designed with an eye to the type of purposive- rational action, so that all other actions can be classified as specific deviations from this type. Weber also analyzes the method of Sinnverstehen in such a way that complex cases can be related to the limit case of understanding purposive-rational action; understanding action that is subjectively oriented to success requires at the same time that it be objectively evaluated as to its correctness […] Habermas, The Theory of Communicative Action, Vol 1, p.6

They solved the problem of connecting Marx and Weber by leaning all the more heavily on Weber. If, following Weber, one conceives of the rationalization of life's orders as the institutionalization of purposive rational action, it is only a small step to generalizing the reification of consciousness into an expression of instrumental reason. And if, like him, one sees the subsystems of purposive rational action irresistibly congealing into an iron cage, it is only a small step from Lukacs's theory of reification to the critique of instrumental reason, that is, to the vision of an administered, totally reified world in which means-ends rationality and domination are merged. This theory has the advantage of directing our attention to the symptoms of the systemically induced deformation of communicatively structured life- contexts, which is no longer localizable in any class-specific way. Its weakness consists in deriving the erosion of the lifeworld from the spell of a means-ends rationality that has been demonized as instrumental reason. The critique of instrumental reason thereby falls into the same error as the Weberian theory and, in addition, forfeits the fruits of an approach nonetheless directed to systemic effects. The concept of instrumental reason suggests that the rationality of knowing and acting subjects is systemically expanded into a purposive rationality of a higher order. Thus the rationality of self-regulating systems, whose imperatives override the consciousness of the members integrated into them, appears in the shape of a totalized purposive rationality. This confusion of system rationality and action rationality prevented Horkheimer and Adorno, as it did Weber before them, from adequately separating the rationalization of action orientations within the framework of a structurally differentiated lifeworld from the expansion of the steering capacity of differentiated social systems. As a result, they could locate the spontaneity that was not yet in the grips of the reifying force of systemic rationalization only in irrational powers in the charismatic power of the leader or in the mimetic power of art and love. Horkheimer and Adorno failed to recognize the communicative rationality of the lifeworld that had to develop out of the rationalization of worldviews before there could be any development of formally organized domains of action at all. It is only this communicative rationality, reflected in the self-understanding of modernity, that gives an inner logic - and not merely the impotent rage of nature in revolt - to resistance against the colonization of the lifeworld by the inner dynamics of autonomous systems. Horkheimer and Adorno were unable to appropriate the systematic content of Weber's diagnosis of the times and to make it fruitful for social-scientific inquiry, because they did not take seriously enough Weber's studies on the rationalization of worldviews, or the independent logic of cultural modernity; but also because they were uncritical in two directions; - vis-à-vis Marx, in that they held fast to the basic assumptions of the theory of value as the core of their tacit orthodoxy, and in this way they blinded themselves to the realities of a developed capitalism based on the pacification of class conflict through welfare-state mea- sures; - vis-à-vis Weber, in that they remained fixated on the model of purposive rationality and, for that reason, did not expand the critique of instrumental reason into a critique of functionalist reason.

The critique of instrumental reason, which remains bound to the conditions of the philosophy of the subject, denounces as a defect something that it cannot explain in its defectiveness because it lacks a conceptual framework sufficiently flexible to capture the integrity of what is destroyed through instrumental reason. To be sure, Horkheimer and Adorno do have a name for it: mimesis. And even though they cannot provide a theory of mimesis, the very name calls forth associations—and they are intended: Imitation designates a relation between persons in which the one accommodates to the other, identifies with the other, empathizes with the other. There is an allusion here to a relation in which the surrender of the one to the example of the other does not mean a loss of self but a gain and an enrichment. Because the mimetic capacity escapes the conceptual framework of cognitive-instrumentally determined subject-object relations, it counts as the sheer opposite of reason, as impulse. Adorno does not simply deny to the latter any cognitive function. In his aesthetics he attempts to show what the work of art owes to the power of mimesis to unlock, to open up. But the rational core of mimetic achievements can be laid open only if we give up the paradigm of the philosophy of consciousness—namely, a subject that represents objects and toils with them—in favor of the paradigm of linguistic philosophy—namely, that of intersubjective understanding or communication—and puts the cognitive-instrumental aspect of reason in its proper place as part of a more encompassing communicative rationality. Habermas, The Theory of Communicative Action, Vol 1, p.389-390

Weber 'parts company with a theory of communicative action' when he defines action in terms of the actor attaching a subjective meaning to it. He does not elucidate "meaning" in connection with the model of speech; he does not relate it to the linguistic medium of possible understanding, but to the beliefs and intentions of an acting subject, taken to being with in isolation. This leads him to his familiar distinction between value-rational, purposive-rational, traditional and affectual action. What Weber should have done instead was to concentrate not on orientations of action but on the general structures of the lifeworld to which acting subjects belong.  William Outhwaite, Habermas: Key Contemporary Thinkers, 1988 in https://en.wikipedia.org/wiki/Rationalization_(sociology)

In analyzing this hopeless situation, Horkheimer and Adorno keyed in on a factor that Weber had singled out: the spread of formal, means/ends rationality, which they called instrumental reason. In doing so, they completely revised Marx's positive evaluation of scientific-technological progress. What for him represented an unambiguously emancipatory potential, for them was the core of a domination generalized to all spheres of life. Subjects who, in Horkheimer's words, "have to form themselves, body and soul, in relation to the technical apparatus" are no longer potential subjects of revolution (1:353). This was empirically borne out by the collapse of the revolutionary labor movement in all industrial societies and by the dis- appearance of the proletariat into the pores of consumer society. Thus the scientific-technological progress that Marx connected with the unleashing of productive forces and the overthrow of capitalism had for Horkheimer and Adorno the ironic effect of immobilizing the very subjective forces that were supposed to accomplish this overthrow. As Horkheimer put it, "All life today tends to be increasingly subjected to rationalization and planning… The individual's self-preservation presupposes his adjustment to the requirements for the preservation of the system". Given this pessimistic diagnosis, it is not surprising that they saw little hope of changing things. Critical theory became resignative, contemplative. It could, at best, disclose the unreason at the heart of what passes for reason, without offering any positive account of its own. McCarthy, Translator’s Introduction, The Theory of Communicative Action, Vol.1, p.xix

In Habermas's view, the dead end in which critical theory thus found itself is by no means unavoidable. To avoid it requires, however, a fundamental shift of paradigm away from the philosophy of consciousness, in which the critique of rationalization as reification from Lukacs to Adorno remained rooted in spite of itself. There are two steps to this shift: first a move from the (monological) teleological concept of action to the concepts of communicative action and lifeworld; and second a joining of the lifeworld perspective to that of systems theory. In Chapter V, which opens Volume 2, Habermas approaches these tasks through a consideration of the work of George Herbert Mead and Emile Durkheim. In the former he finds the essential elements of a communications-theoretic reformulation of social-action theory; in the latter, the lineaments of a theory that links social integration with system integration. McCarthy, Translator’s Introduction, The Theory of Communicative Action, Vol.1, p.xix