We present Hubble Space Telescope WFC3/UVIS (F275W, F336W) and ACS/WFC optical (F435W, F555W, and F814W) observations of the nearby grand-design spiral galaxy M101 as part of the Legacy Extragalactic UV Survey (LEGUS). Compact sources detected in at least four bands were classified by both human experts and the convolutional neural network StarcNet. Human experts classified the 2351 brightest sources, retrieving N c = 965 star clusters. StarcNet, trained on LEGUS data not including M101, classified all 4725 sources detected in four bands, retrieving N c = 2270 star clusters. The combined catalog represents the most complete census to date of compact star clusters in M101. We find that for the 2351 sources with both a visual- and machine-learning classification StarcNet is able to reproduce the human classifications at high levels of accuracy (∼80%-90%), which is equivalent to the level of agreement between human classifiers in LEGUS. The derived cluster age distribution implies a disruption rate of dN / d τ ∝ τ − 0.45 ± 0.14 over 107 < τ < 108.5 yr for cluster masses ≥103.55 M ⊙ for the central region of M101 and dN / d τ ∝ τ − 0.02 ± 0.15 for cluster masses ≥103.38 M ⊙ in the northwest region of the galaxy. The trends we recover are weaker than those of other nearby spirals (e.g., M51) and starbursts, consistent with the M101 environment having a lower-density interstellar medium, and providing evidence in favor of environmentally dependent cluster disruption in the central, southeast, and northwest regions of M101.