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.
The West Ham striker was quick to vent his apparent disappointment at the verdict on Twitter, with a post on the social media site which simply read: "DISGRACEFUL!!!"
DISGRACEFUL!!! 😡- Andy Carroll (@AndyTCarroll) February 4, 2014
Flores should get banned for carrying on like a school girl. Carroll did swing his arm intentionally, but it was after Flores was climbing all over him and had his arm wrapped around Carroll's head. It was a soft red card, and a even worse decision to stick with the three week suspension. Former manager of the Swans said it was soft. Flores should feel ashamed that reacted like that, it's pathetic. I'm from Australia and a lot of people do not like football because they say the players go down too easy and carry on like they have been shot. Flores is a prime example. Time to harden up and play football and stop carrying on. What ever happened to the mongrel in footballers of the 70's and 80's?- pencil