Monte Carlo coarse-grained simulations of nanogels loaded with nanoparticles are presented, paying special attention to two phenomena revealed by experiments with real composites: the deswelling and charge inversion observed after the absorption of nanoparticles. Both can be justified here exclusively in terms of electrostatic and excluded volume interactions. According to our results, charge inversion in composites presents its own peculiarities. For instance, it only takes place if the charge of the nanoparticle exceeds a threshold value that increases with the nanoparticle size. Simulations also show that the distribution of nanoparticles inside the polyelectrolyte network varies with the nanoparticle charge. In addition, the location of nanoparticles inside the nanogel strongly depends on whether charge inversion occurs.