Referee Howard Webb showed Carroll a red card for catching Swansea defender Chico Flores across the face with his arm at Upton Park.
The Spaniard clutched his face and rolled on the ground, but replays showed that Carroll's arm barely brushed the top of Flores' head.
A West Ham insider told the Daily Mail: "We are incensed by the decision. We'll get a top QC to look at the whole process and see if it is in any way flawed.
"It's a sad day for football when the player who pretended to be hit in full in the face - when he wasn't - comes out the winner.
"We are without Andy for three crucial games, but we have faith in our squad - and in our manager - to get us out of trouble.
"We are only two points behind Swansea in 11th place and so we have to go into these games in a confident frame of mind."
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