We develop a perturbation model to predict the effect of a spatially varying absorptive inhomogeneities in a diffusing slab. The model is based on a perturbation solution of diffusion equation derived for a refractive index mismatch between the scattering slab and the surrounding medium, through the use of the extrapolated boundary conditions. We show that the model allows to compute the time-dependent relative change in the transmitted signal resulting from the presence of the inclusion. We derive simplified expressions for the perturbed time-resolved transmittance that allows to implement an efficient fitting procedure for obtaining the optical properties of the absorptive inclusion. The accuracy of the predictions of the model was investigated through comparison with the results of the Finite Element Method to solve the time-dependent diffusion equation numerically. The procedure is used to obtain the absorption perturbation parameter of an absorptive inclusion characterized by spatially dependent Gaussian distribution of its absorption coefficient located at the midplane of a scattering slab.