The COMET experiment aims to search for the neutrinoless muon to electron transition process with new sensitivity levels. The online trigger system is an integral part of achieving the sensitivity levels required and will be subject to an expected neutron fluence of up to $10^{12}$ $n \cdot \mathrm{cm}^{-2}\;$ within regions inside the detector solenoid. Consequently a significant number of soft errors in the logic of the onboard field programmable gate arrays (FPGA) can occur, requiring error correction for single event upsets and firmware reprogramming schemes for unrecoverable soft errors. We studied the radiation tolerance of the COMET Phase-I front-end trigger system, called COTTRI, subject to neutron fluence on order $10^{12}$ $n \cdot \mathrm{cm}^{-2}\;$ with multiple error correcting codes and automatic firmware reconfiguration. The regions measured were the configuration RAM, block RAM and also in a multi-gigabit transfer link using copper cables that will be used for communication between different trigger boards during Phase-I. The resulting cross sections observed suggest the most significant impact to the experiment will come from unrecoverable soft errors in configuration RAM, with dead time expected to be $(4.2 \pm 1.3)\%$. The effect of multi-bit errors in block RAM was found to be almost negligible in COMET Phase-I. In addition, multiple solutions have already been proposed in order to suppress these errors further. Soft errors observed in the multi-gigabit transfer links were measured to be of two orders of magnitude less impact compared to the unrecoverable errors in configuration RAM. We concluded that the COTTRI system meets the trigger requirement in COMET Phase-I.