Compact groups of galaxies are devised as extreme environments where interactions may drive galaxy evolution. In this work, we analysed whether the luminosities of galaxies inhabiting compact groups differ from those of galaxies in loose galaxy groups. We computed the luminosity functions of galaxy populations inhabiting a new sample of 1412 Hickson-like compact groups of galaxies identified in the Sloan Digital Sky Survey Data Release 16. We observed a characteristic absolute magnitude for galaxies in compact groups brighter than that observed in the field or loose galaxy systems. We also observed a deficiency of faint galaxies in compact groups in comparison with loose systems. Our analysis showed that the brightening is mainly due to galaxies inhabiting the more massive compact groups. In contrast to what is observed in loose systems, where only the luminosities of Red (and Early) galaxies show a dependency with group mass, luminosities of Red and Blue (also Early and Late) galaxies in compact groups are affected similarly as a function of group virial mass. When using Hubble types, we observed that elliptical galaxies in compact groups are the brightest galaxy population, and groups dominated by an elliptical galaxy also display the brightest luminosities in comparison with those dominated by spiral galaxies. Moreover, we show that the general luminosity trends can be reproduced using a mock catalogue obtained from a semi-analytical model of galaxy formation. These results suggest that the inner extreme environment in compact groups prompts a different evolutionary history for their galaxies.