We analyze by means of finite-element numerical calculations the polarization force between a sharp conducting tip and a non-spherical uncharged dielectric nanoparticle with the objective of quantifying its dielectric constant from electrostatic force microscopy (EFM) measurements. We show that for an oblate spheroid nanoparticle of given height the strength of the polarization force acting on the tip depends linearly on the eccentricity, e, of the nanoparticle in the small eccentricity and low dielectric constant regimes (1 < e < 2 and 1 < ε(r) < 10), while for higher eccentricities (e > 2) the dependence is sub-linear and finally becomes independent of e for very large eccentricities (e > 30). These results imply that a precise account of the nanoparticle shape is required to quantify EFM data and obtain the dielectric constants of non-spherical dielectric nanoparticles. Experimental results obtained on polystyrene, silicon dioxide and aluminum oxide nanoparticles and on single viruses are used to illustrate the main findings.