We present deep, narrowband imaging of the nearby spiral galaxy M101 and its group environment to search for star-forming dwarf galaxies and outlying HII regions. Using the Burrell Schmidt telescope, we target the brightest emission lines of star-forming regions, H$\alpha$, H$\beta$, and [OIII], to detect potential outlying star-forming regions. Our survey covers ~6 deg$^{2}$ around M101, and we detect objects in emission down to an Hα flux level of $5.7 × 10^{-17}$ erg s$^{-1}$ cm$^{-2}$ (equivalent to a limiting star formation rate of $1.7 × 10^{-6}$ $M_\odot$ yr$^{-1}$ at the distance of M101). After careful removal of background contaminants and foreground M stars, we detect 19 objects in emission in all three bands and 8 objects in emission in Hα and [OIII]. We compare the structural and photometric properties of the detected sources to Local Group dwarf galaxies and star-forming galaxies in the 11HUGS and SINGG surveys. We find no large population of outlying HII regions or undiscovered star-forming dwarfs in the M101 Group, as most sources (93%) are consistent with being M101 outer-disk HII regions. Only two sources were associated with other galaxies: a faint star-forming satellite of the background galaxy NGC 5486 and a faint outlying HII region near the M101 companion NGC 5474. We also find no narrowband emission associated with recently discovered ultradiffuse galaxies and starless H I clouds near M101. The lack of any hidden population of low-luminosity star-forming dwarfs around M101 suggests a rather shallow faint-end slope (as flat as $\alpha ~ -1.0$) for the star-forming luminosity function in the M101 Group. We discuss our results in the context of tidally triggered star formation models and the interaction history of the M101 Group.