The West Ham manager criticised referee Phil Dowd for failing to award his side a penalty during an FA Cup defeat at Manchester United.
Allardyce denied the charge and sought a personal hearing, but a panel decided his comments were in breach of FA Rule E3 and he was also warned about his future conduct.
Dowd gave United a penalty for a Jordan Spence handball but turned down West Ham appeals for handball against Rafael da Silva in an incident Allardyce called "very similar".
He said at the time: "There's no doubt about the difference between Rafael's handball and 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.
"He (Dowd) couldn't find the courage to give it, unfortunately, and there was a very similar incident with Jordan Spence and it was given.
"You have to have the courage 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."
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