Charge transfer and electron-phonon coupling (EPC) are proposed to be two important constituents associated with enhanced superconductivity in the single unit cell FeSe films on oxide surfaces. Using high-resolution electron energy loss spectroscopy combined with first-principles calculations, we have explored the lattice dynamics of ultrathin FeSe films grown on SrTiO3. We show that, despite the significant effect from the substrate on the electronic structure and superconductivity of the system, the FeSe phonons in the films are unaffected. The energy dispersion and linewidth associated with the Fe- and Se-derived vibrational modes are thickness- and temperature-independent. Theoretical calculations indicate the crucial role of antiferromagnetic correlation in FeSe to reproduce the experimental phonon dispersion. Importantly, the only detectable change due to the growth of FeSe films is the broadening of the Fuchs-Kliewer (F-K) phonons associated with the lattice vibrations of SrTiO$_3$(001) substrate. If EPC plays any role in the enhancement of film superconductivity, it must be the interfacial coupling between the electrons in FeSe film and the F-K phonons from substrate rather than the phonons of FeSe.