The covariant particle-vibration coupling model within the time-blocking approximation is employed to supplement the relativistic random phase approximation (RRPA) with coupling to collective vibrations. The Bethe-Salpeter equation in the particle-hole channel with an energy-dependent residual particle-hole (ph) interaction is formulated and solved in the shell-model Dirac basis as well as in the momentum space. The same set of coupling constants generates the Dirac-Hartree single-particle spectrum, the static part of the residual ph interaction, and the particle-phonon coupling amplitudes. This approach is applied to a quantitative description of damping phenomenon in even-even spherical nuclei with closed shells ²⁰⁸Pb and ¹³²Sn. Since phonon coupling enriches the RRPA spectrum with a multitude of ph ⊗ phonon states, a noticeable fragmentation of giant monopole and dipole resonances is obtained in the examined nuclei. The results are compared with experimental data and results of the nonrelativistic approach.