We have obtained deep Hubble Space Telescope (HST) imaging of four faint and ultra-faint dwarf galaxy candidates in the vicinity of M101 - Dw21, Dw22, Dw23 and Dw35, originally discovered by Bennet et al. (2017). Previous distance estimates using the surface brightness fluctuation technique have suggested that these four dwarf candidates are the only remaining viable M101 satellites identified in ground based imaging out to the virial radius of M101 (D~250 kpc). Advanced Camera for Surveys imaging of all four dwarf candidates shows no associated resolved stellar populations, indicating that they are thus background galaxies. We confirm this by generating simulated HST color magnitude diagrams of similar brightness dwarfs at the distance of M101. Our targets would have displayed clear, resolved red giant branches with dozens of stars if they had been associated with M101. With this information, we construct a satellite luminosity function for M101, which is 90% complete to M_V=-7.7 mag and 50% complete to M_V=-7.4 mag, that extends into the ultra-faint dwarf galaxy regime. The M101 system is remarkably poor in satellites in comparison to the Milky Way and M31, with only eight satellites down to an absolute magnitude of M_V=-7.7 mag, compared to the 14 and 26 seen in the Milky Way and M31, respectively. Further observations of Milky Way analogs are needed to understand the halo-to-halo scatter in their faint satellite systems, and connect them with expectations from cosmological simulations.
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