We present single-shot electron velocity-map images of nanoplasmas generated from doped helium nanodroplets and neon clusters by intense near-infrared and mid-infrared laser pulses. We report a large variety of signal types, most crucially depending on the cluster size. The common feature is a two-component distribution for each single-cluster event: A bright inner part with nearly circular shape corresponding to electron energies up to a few eV, surrounded by an extended background of more energetic electrons. The total counts and energy of the electrons in the inner part are strongly correlated and follow a simple power-law dependence. Deviations from the circular shape of the inner electrons observed for neon clusters and large helium nanodroplets indicate non-spherical shapes of the neutral clusters. The dependence of the measured electron energies on the extraction voltage of the spectrometer indicates that the evolution of the nanoplasma is significantly affected by the presence of an external electric field. This conjecture is confirmed by molecular dynamics simulations, which reproduce the salient features of the experimental electron spectra. © 2021 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.