Incensed that the Hammers had not been awarded a penalty during their 1-0 defeat, Allardyce suggested that referee Phil Dowd had favoured the home side as he had awarded United a spot kick for a similar incident just moments later.
However, Allardyce’s comments have been deemed as a breach of FA rules and the 58-year-old has until Wednesday to respond to the charge.
A statement from the FA read: "West Ham United manager Sam Allardyce has been charged with misconduct in relation to media comments following this week’s FA Cup with Budweiser third round replay against Manchester United at Old Trafford.
"The charge is in relation to an alleged breach of FA Rule E3 concerning 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."
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After watching his side lose at Old Trafford in their third round replay, Allardyce’s remarks were critical of Dowd's performance and suggested that West Ham were equally deserving of a penalty.
His exact post-match comments were: "The one difference between Rafael’s handball and Spence’s was that Jordan plays for West Ham away against Manchester United and Rafael plays at home at Old Trafford.
"It's got to be that simple. Phil Dowd was in the perfect position. Rafael pushes the ball away with his left arm. No penalty. Go to the other end and the ball hits Jordan’s hand. If you give one you have to give both, simple as that."