Within the framework of a model representing the potential of a C-60 cage as a spherical electro-neutral layer U(r) formed by smeared carbon atoms, the effect of the details of the potential on spectral characteristics of atoms localized inside the fullerene shell has been studied. Using examples of encapsulated H and He atoms, it is shown that for potential shell thickness not exceeding 1.3-1.5 au, confinement resonance oscillations in the photoionization cross section weakly depend on the shape of the function U(r). With increasing width of the potential well, the confinement resonances in the energy dependence of the photoionization cross section disappear. In addition, it is demonstrated that displacing the doped atom from the centre of the cavity also diminishes the amplitude of the confinement resonance.