Hinds was shown a straight red in stoppage time of the loss to Tranmere.
United launched an appeal after speaking to match referee Jonathan Moss.
But a three-man FA panel has upheld the card, which means he must serve a three-game ban.
Weather permitting, it means he misses the League game against Brentford, LDV Vans Trophy match with Halifax and FA Cup second round trip to Aldershot Town.