Chelsea immediately lodged an appeal against the decision but an FA commission rejected their claim and Mikel will have to serve a three-match ban for serious foul play.
The FA said in a statement: "At a regulatory commission hearing today, a claim for wrongful dismissal from Chelsea's Mikel John Obi was rejected.
"Mikel was shown a red card for serious foul play during the match at Old Trafford on 23 September.
"As a result, Mikel will serve a three-match suspension with immediate effect."
To have succeeded in their appeal the club would have had to prove that there should not have been any form of sanction taken against the player, and that in effect there had been a clear error by the referee.