Allardyce reacted angrily to Phil Dowd's decision to award Manchester United a penalty for handball after West Ham were denied one for a similar offence by Rafael at the other end.
In a statement, the FA said Allardyce has until Wednesday 23 January to respond to the charge.
West Ham lost the match 1-0 to a Wayne Rooney goal, but the England striker missed the chance to add a second from the penalty spot. United were awarded the spot-kick after Jordan Spence handled the ball in similar fashion to Rafael before the break.
Speaking on ITV after the match, a furious Allardyce said: "There's no doubt about the difference between Rafael's handball and Jordan Spence's.
"Spence plays for West Ham and the away team, while Rafael plays for the home side at Old Trafford."
He added: "You see it time and time again at Old Trafford."
Later in his press conference, Allardyce continued his complaint, saying: "He couldn't find the courage to give it unfortunately, and he then went down the other end and there was a very similar incident with Jordan Spence and it was given. That is a very big disappointment for me - the lack of consistency in that area."
He continued: "I think you have to have courage to play here and to referee here.
"But why are you a professional referee or player? To come to these places to do your job, and do it to the best of your ability. Phil Dowd is a hugely experienced referee and one of the top ones in this country, but I have to say he did get it wrong."