Following the result of Friday's decision, the striker, who was dismissed for a clash with Chico Flores, will now miss fixtures against Aston Villa, Norwich City and Southampton
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The club's initial attempt to have the striker's suspension withdrawn was rejected by the Football Association, which resulted in West Ham taking their appeal to a further hearing on Friday.
Following the result of the decision by the tribunal, Carroll will now miss fixtures against Aston Villa, Norwich City and Southampton.
Carroll was dismissed by referee Howard Webb in last Saturday's 2-0 victory over Swansea City, after it was adjudged he swung an arm into the face of Chico Flores.
The Swansea defender went to ground and clutched his face but replays showed Carroll's arm brushing the top of the Spaniard's head.
Sam Allardyce claimed West Ham had been the victim of "injustice" at his pre-match press conference ahead of Saturday's encounter with Aston Villa.