We have carried out a study of the X-ray properties of the supernova remnant (SNR) population in M33 with XMM-Newton, comprising deep observations of eight fields in M33 covering all of the area within the D_25_ contours, and with a typical luminosity of 7.1x10^34^erg/s (0.2-2.0keV). Here, we report our work to characterize the X-ray properties of the previously identified SNRs in M33, as well as our search for new X-ray detected SNRs. With our deep observations and large field of view we have detected 105 SNRs at the 3{sigma} level, of which 54 SNRs are newly detected in X-rays, and three are newly discovered SNRs. Combining XMM-Newton data with deep Chandra survey data allows detailed spectral fitting of 15 SNRs, for which we have measured temperatures, ionization time-scales and individual abundances. This large sample of SNRs allows us to construct an X-ray luminosity function, and compare its shape to luminosity functions from host galaxies of differing metallicities and star formation rates to look for environmental effects on SNR properties. We conclude that while metallicity may play a role in SNR population characteristics, differing star formation histories on short time-scales, and small-scale environmental effects appear to cause more significant differences between X-ray luminosity distributions. In addition, we analyse the X-ray detectability of SNRs, and find that in M33 SNRs with higher [SII]/H{alpha} ratios, as well as those with smaller galactocentric distances, are more detectable in X-rays.