The Hammers appealed against Carroll's dismissal for an altercation with Swansea defender Chico Flores but it was rejected by an independent three-person panel.
Carroll was shown a straight red card by referee Howard Webb in the second half of the Hammers' 2-0 win and video footage of the incident, as well as written evidence from the Hammers and match officials, was assessed by the panel.
A three-match suspension rules Carroll out for the rest of February and matches with Aston Villa, Norwich and Southampton.
The 25-year-old made just his third start of the season following a heel injury and set up both goals for Kevin Nolan in the 2-0 victory.
Hammers manager Sam Allardyce declared his intention to contest Carroll's dismissal after the match and was critical of Flores.
Allardyce said: "We will hope that the appeal will work. Hopefully we don't lose Andy for three games.
"He's gutted. He's absolutely beside himself. We'll just have to go through the process and see what happens in midweek.
"All I can hope is that the panel, in the cold light of day, see it for what it is.
"He (Webb) can't be absolutely certain of what's happened, except that Chico Flores is over-exaggerating, which is generally the norm for him, unfortunately."
The absence of West Ham's club-record signing has been one of the major factors in their poor first half to the season, which has seen them in a constant battle to steer clear of the Premier League bottom three.
Now sitting 18th, just a point inside the relegation zone, Carroll's return to the side injected a much-needed impetus into their faltering campaign.
The former Newcastle and Liverpool forward set up a goal on his return from his long-standing foot problem in the 2-0 win at Cardiff and, with heavy home defeats to the Magpies and Manchester City preceding a hard-fought draw at Chelsea, Carroll once again showed his value in creating both goals for Nolan in the vital win over Swansea.
But now Allardyce will be without his talisman once more, with Carlton Cole and Marco Borriello fighting it out to replace Carroll in the starting line-up for the weekend trip to Villa Park.