Recent radio surveys have discovered a large number of low luminosity core dominated radio galaxies that are much more abundant than those at higher luminosities. These objects will be too faint in gamma-rays to be detected individually by Fermi. Nevertheless, they may contribute significantly to the unresolved extragalactic gamma-ray background. We consider here the possible contribution of these core dominated radio galaxies to the diffuse extragalactic gamma-ray background. Using published data available for all 45 of the radiogalaxies listed as detected counterparts in the Fermi FL8Y source list update to the 3FGL catalog, we have searched for radio maps which can resolve the core flux from the total source flux. Using high resolution radio maps we were able to obtain core fluxes for virtually every source. We then derived a relation between core radio flux and gamma-ray flux that we extrapolated to sources with low radio luminosities that are known to be highly core dominated. We then employed a very recent determination of the luminosity function for core dominated radio galaxies in order to obtain the contribution of all possible gamma-ray emitting radio galaxies to the unresolved extragalactic gamma-ray background. We find this contribution to be a possibly non-negligible, 4% - 18% of the background.