Stimulated Raman interaction of a classically pumped single three-level $\Lambda$-type atom in a resonator cavity featuring both radiative and unwanted losses is studied. It is shown that in the regime of stimulated adiabatic Raman passage the excited outgoing wave packet of the cavity-assisted electromagnetic field can be prepared in a one-photon Fock state with high efficiency. In this regime, the spatio-temporal shape of the wave packet does not depend on the interaction shape of the pump field, provided that the interaction of the atom with the pump is time-delayed with respect to the interaction of the atom with the cavity-assisted field. Therefore, the scheme can be used to generate a sequence of identical radiation pulses each of almost one-photon Fock state. It is further shown that the spatio-temporal shape of the outgoing wave packet can be manipulated by controlling the time of interaction between the atom and the cavity-assisted electromagnetic field.