The London club went out of the FA Cup with Wayne Rooney leading his side to a 1-0 victory, but the Hammers manager fumed over contentious handball decisions at either end
Rafael appeared to handle the ball in his own area but the visitors' claims for a spot kick were waved away by referee Phil Dowd, while Wayne Rooney skied a late penalty after Jordan Spence used his arm to block a Ryan Giggs cross.
Despite neither incident resulting in a goal - with Rooney settling the tie after being set up by Chicharito after nine minutes - the Hammers manager feels the league leaders get preferential treatment at home.
"There's no doubt whatsoever about the difference between Rafael's handball and Jordan Spence's - Jordan Spence plays for West Ham away against Man United and Rafael plays at home at Old Trafford; it's got to be that simple when you see it," he told ITV after the game.
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"You go the other end, Jordan Spence's arm comes up, [the] ball hits his hand, [Dowd] gives the penalty; if you're gonna give one you've got to give them both."
When pressed on whether United get the majority of the decisions when playing at home, Allardyce left it in no doubt that he thinks Sir Alex Ferguson's team get the benefit of the doubt at Old Trafford.
"Well, you've seen it for yourself, haven't you? you look at the replays as many times as you want. You look at the referee's position," he continued.
"I've looked at [Dowd's] position and it's perfect, straight in line with it and straight in front of it. He had a worse position than Jordan Spence's to see that one than he did on Rafael's."