We theoretically investigate the coupling between molecular excitons and dipolar Fano-like cavity plasmon resonance in two-layered core-shell resonators consisting of a dielectric core with high refractive index and a thin metal outer shell gapped by a low refractive index thin dielectric layer containing molecules. We demonstrate that associated with the excitation of the dipolar Fano-like cavity plasmon, the electric fields can be highly localized within the dielectric gap shell, leading to very small mode volumes. By using the three-oscillator temporal coupled model to describe the proposed plasmon-exciton system, we are able to demonstrate that the coupling between molecular excitons and cavity plasmon resonance can reach the strong coupling regime. Furthermore, we also demonstrate that reducing the thickness or the refractive index of the dielectric gap shell layer can result in further compression of the mode volumes, and consequently decrease the minimum number of the coupled excitons that are required to fulfill the criteria for strong coupling.