When a quasi-monochromatic wave propagating in an inhomogeneous magnetoplasma has sufficiently large amplitude, there exist phase-trapped resonant particles whose energy increases or decreases depending on the "sign" of inhomogeneity. The variation of energy density of such particles can greatly exceed the wave energy density which contradicts energy conservation under the prevalent assumption that the wave serves as the energy source or sink. We show that, in fact, the energy increase (or decrease) of phase-trapped particles is related to energy transfer from (to) phase untrapped particles, while the wave basically mediates the energization process. Virtual importance of this comprehension consists in setting proper quantitative constraints on attainable particle energy. The results have immediate applications to at least two fundamental problems in the magnetospheric physics, i.e. particle dynamics in the radiation belts and whistler-triggered emissions.