We model the emission spectrum of a quantum dot embedded in a (e.g. photonic crystal) nanocavity, using a semi-classical approach to describe the matter-field interaction. We start from the simple model of a quantum dot as a two-level system, and recover the result expected from cavity quantum electrodynamics. Then, we study the influence of electron-acoustic-phonons interaction. We show that the surrounding semiconductor plays an essential role in the emission spectrum in strong coupling.