The generation and manipulation of single photons are crucial in advanced quantum technologies, such as quantum communication and quantum computation devices. High-purity single photons can be generated from classical light using the single-photon blockade (1PB). However, the efficiency and purity are exclusive in 1PB, which hinders its practical applications. Here, we show that the resonantly coupled plasmonic-photonic cavity can boost the efficiency of single-photon generation by more than three orders of magnitude compared with that of all-dielectric microcavity. This significant improvement is attributed to two new mechanisms of atom-microcavity coupling after introducing the plasmonic cavity: the formation of a quasi-bound state and the transition to the nonreciprocal regime, due to the destructive interference between the coupling pathways and the nonzero relative phase of the closed-loop coupling, respectively. The quasi-bound state has a relatively small decaying, while its effective coupling strength is significantly enhanced. Suppressing the dissipative component of the effective atom-microcavity coupling in the nonreciprocal regime can further improve single-photon performance, particularly without temporal oscillations. Our study demonstrates the possibility of enhancing the intrinsically low efficiency of 1PB in low excitation regime, and unveils the novel light-matter interaction in hybrid cavities.single-photon blockade, atom-photon quasi-bound state, plasmonic-photonic cavity