We present measurements of the galaxy luminosity and stellar mass function in a 3.71 deg(2) (0.3Mpc(2)) area in the core of the Virgo Cluster, based on u*griz data from the Next Generation Virgo Cluster Survey (NGVS). The galaxy sample-which consists of 352 objects brighter than M-g = -9.13 mag, the 50% completeness limit of the survey-reaches 2.2 mag deeper than the widely used Virgo Cluster Catalog and at least 1.2 mag deeper than any sample previously used to measure the luminosity function in Virgo. Using a Bayesian analysis, we find a best-fit faint-end slope of alpha = -1.33 +/- 0.02 for the g-band luminosity function; consistent results are found for the stellar mass function and the luminosity function in the other four NGVS bandpasses. We discuss the implications for the faint-end slope of adding 92 ultracompact dwarfs (UCDs)-previously compiled by the NGVS in this region-to the galaxy sample, assuming that UCDs are the stripped remnants of nucleated dwarf galaxies. Under this assumption, the slope of the luminosity function (down to the UCD faint magnitude limit, M-g = -9.6mag) increases dramatically, up to alpha = -1.60 +/- 0.06 when correcting for the expected number of disrupted non-nucleated galaxies. We also calculate the total number of UCDs and globular clusters that may have been deposited in the core of Virgo owing to the disruption of satellites, both nucleated and non-nucleated. We estimate that similar to 150 objects with M-g less than or similar to -9.6 mag and that are currently classified as globular clusters might, in fact, be the nuclei of disrupted galaxies. We further estimate that as many as 40% of the (mostly blue) globular clusters in the Virgo core might once have belonged to such satellites; these same disrupted satellites might have contributed similar to 40% of the total luminosity in galaxies observed in the core region today. Finally, we use an updated Local Group galaxy catalog to provide a new measurement of the luminosity function of Local Group satellites, alpha = -1.21 +/- 0.05, which is only 1.7 sigma shallower than measured in the core of the Virgo Cluster.