We investigate numerically the kinetics of diffusion limited annihilation reactions in disordered binary square lattices where the reacting particles are constrained to diffuse on a concentration of the lattice sites. We find that the asymptotic decay of the particle concentration in the percolative regime is of the form c(t,p)-c(r)(p) alpha t(-ds/2), where c(r)(p) is the concentration of residual particles. We recover well known results such as d(s)(p>p(c))=d=2 with logarithmic corrections, and d(s)(p(c))=1.34+/-0.02. For p singlet) on isotopic mixed crystals of naphthalene.