The 25-year-old England forward was sent off by referee Howard Webb following a tussle with Swansea's Chico Flores, having set up both of Kevin Nolan's goals as the Hammers picked up just their fifth Barclays Premier League win of the season.
Carroll sent a Tweet on Tuesday afternoon suggesting he was aware of the decision as he simply wrote: "DISGRACEFUL".
He will now miss the Hammers' next three fixtures, starting with Saturday's clash with Aston Villa, after only featuring in four league games so far this season following a lengthy injury lay-off.
The Football Association clarified the reasoning behind the decision not to overturn Webb's decision in a short statement on its official website.
"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'," it read.
"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."
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 - with the striker also suspended for the home matches against Norwich and Southampton.