Post-cognitive approaches to cognitive science, such as enactivism and autopoietic theory, are typically assumed to involve the rejection of computationalism. We will argue that this assumption results from the conflation of computation with the notion of representation, which is ruled out by the post-cognitivist rejection of cognitive realism. However, certain theories of computation need not invoke representation, and are not committed to cognitive realism, meaning that post-cognitivism need not necessarily imply anti-computationalism. Finally, we will demonstrate that autopoietic theory shares a mechanistic foundation with these theories of computation, and is therefore well-equipped to take advantage of these theories.