The typical detection rate of ~1 gamma-ray burst (GRB) per day by the Fermi Gamma-ray Burst Monitor (GBM) provides a valuable opportunity to further our understanding of GRB physics. However, the large uncertainty of the Fermi localization typically prevents rapid identification of multiwavelength counterparts. We report the follow-up of 93 Fermi GRBs with the Gravitational-wave Optical Transient Observer (GOTO) prototype on La Palma. We selected 53 events (based on favourable observing conditions) for detailed analysis, and to demonstrate our strategy of searching for optical counterparts. We apply a filtering process consisting of both automated and manual steps to 60 085 candidates initially, rejecting all but 29, arising from 15 events. With ≍3 GRB afterglows expected to be detectable with GOTO from our sample, most of the candidates are unlikely to be related to the GRBs. Since we did not have multiple observations for those candidates, we cannot confidently confirm the association between the transients and the GRBs. Our results show that GOTO can effectively search for GRB optical counterparts thanks to its large field of view of ≍40 deg2 and its depth of ≍20 mag. We also detail several methods to improve our overall performance for future follow-up programmes of Fermi GRBs.