Electron energy-loss spectroscopy (EELS) has become increasingly popular for detailed characterization of plasmonic nanostructures, owing to the unparalleled spatial resolution of this technique. The typical setup in EELS requires nanoparticles to be supported on thin substrates. However, as in optical measurements, the substrate material can modify the acquired signal. Here, we have investigated how the EELS signal recorded from supported silver and gold spheroidal nanoparticles at different electron beam impact parameter positions is affected by the choice of a dielectric substrate material and thickness. Consistent with previous optical studies, the presence of a dielectric substrate is found to red-shift localized surface plasmons, increase their line widths, and lead to increased prominence of higher order modes. The extent of these modifications heightens with increasing substrate permittivity and thickness. Specific to EELS, the results highlight the importance of the beam impact parameter and substrate-related C ̌erenkov losses and charging. Our experimental results are compared with and corroborated by full-wave electromagnetic simulations based on the boundary element method. The results present a comprehensive study of substrateinduced modifications in EELS and allow identification of optimal substrates relevant for EELS studies of plasmonic structures.