Allardyce had until Wednesday afternoon to respond to the charge and the FA has confirmed his denial.
The Hammers boss reacted angrily to referee 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.
A statement from the FA read: "West Ham United manager Sam Allardyce has denied an FA charge of misconduct in relation to media comments. The comments followed his side's FA Cup with Budweiser third round replay against Manchester United at Old Trafford on January 16, 2013.
"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."
A last-gasp Robin van Persie equaliser at Upton Park had forced the replay, which West Ham lost 1-0. Wayne Rooney scored the 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 in an eventful second half.
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. 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 I have to say he did get it wrong."