The 58-year-old was charged for his comments which followed the 1-0 FA Cup third round replay defeat to Manchester United at Old Trafford on 16 January.
Allardyce has requested a personal hearing, the date of which will be set in due course.
The Hammers boss reacted angrily to referee Phil Dowd's decision to award Manchester United a penalty for handball by Jordan Spence after West Ham were denied one for a similar offence by Rafael at the other end.
In a TV interview after the match, 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. 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.
"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 today I have to say he did get it wrong."
A statement from the FA read: "It is alleged Allardyce questioned the integrity of the match referee and/or match officials in general, and/or implied that the match referee and/or match officials in general were motivated by bias; and/or brought the game into disrepute in contravention of Rule E3(1).
"Allardyce has requested a personal hearing, the date of which will be set in due course."