The problem of catalyst deactivation by active site poisoning and pore blockage, under globally kinetic control, is analyzed. The catalyst pore space is represented by a three-dimensional network of interconnected pores. As a result, the effect of morphological properties of the catalyst pore space, i.e., its geometry (pore size distribution) and topology (connectedness), on the deactivation process is investigated, for the first time, simultaneously. The concepts of percolation theory, a modern theory of statistical physics of disordered media, are employed to show that both single-pore and bundle of parallel pore models perform rather poorly and that the interconnectivity of the pores plays a fundamental role in the overall catalytic behavior. The extension of the model to more complicated systems is also discussed.