The West Ham boss answered his charge by the deadline of Wednesday afternoon and the FA confirmed that the charge had been denied.
During the game, Allardyce was not happy about referee Phil Dowd's decision not to award West Ham a penalty for an offence similar to one that United were given a spot kick.
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."