Batth was shown a straight red card by referee Peter Bankes for a challenge on Hordur Magnusson in the first half of the game at Ashton Gate.
Following the game, Wolves lodged an appeal of wrongful dismissal with the FA that has since been rejected by the independent regulatory commission and, as a result, the 27-year-old will serve his three-match ban in full.
Batth will miss Tuesday night’s game against Brentford, the Third Round Emirates FA Cup tie against Swansea City and the league trip to Barnsley on Saturday, 13th January.