Carroll was dismissed after he was adjudged to have deliberately caught Swansea defender Chico Flores with a flailing arm.
But the Football Association has rejected the appeal and Carroll will now be unavailable to manager Sam Allardyce as he serves a three-match ban.
"West Ham United's Andy Carroll will serve a three-match suspension with immediate effect after his claim of wrongful dismissal was rejected by an Independent Regulatory Commission," read an FA statement.
"Carroll was dismissed for violent conduct during West Ham's game against Swansea City on Saturday (February 1, 2014).
"As stated in the Rules and Regulations of The FA, an Independent Regulatory Commission must apply the test of whether the decision to dismiss a player was 'an obvious error'.
"The decision of an Independent Regulatory Commission in relation to a claim of wrongful dismissal is final and binding on all parties and is not subject to appeal."
Carroll will miss West Ham's away game with Aston Villa on Saturday, as well as home fixtures with Norwich and Southampton.