Allardyce did not hide his annoyance after his side were not awarded what he considered a penalty while United did get a spot kick, a decision he put down to United enjoying home advantage.
West Ham were denied a penalty in the all-Premnier League tie when the ball struck Rafael's arm but the hosts got one when Jordan Spence handled late on although Wayne Rooney missed the spot kick.
"You see it time and time again at Old Trafford," Allardyce had said after Wednesday's 1-0 defeat. "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."
The FA said on its website (www.thefa.com) on Friday that the charge was "in relation to an alleged breach of FA Rule E3".
It concerned: "media comments which 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 are motivated by bias and/or brought the game into disrepute."
Allardyce has until Wednesday to respond to the charge. (Writing by Pritha Sarkar, editing by Ken Ferris)