The Hammers want the Football Association to take the case to an arbitration panel after referee Howard Webb's decision to send off the striker after a clash with Swansea's Chico Flores was upheld by a three-man FA appeal's body.
Carroll is now facing a three-match ban and Gold said that could mean the difference between relegation and top-flight survival.
Gold told Press Association Sport: "We are hugely disappointed at the outcome of the process.
"There is nowhere to go other than to seek some kind of legal redress. It's not ideal, the last thing I want to do is going to some kind of legal issue because I think it is a footballing issue.
"But we are fighting for our lives. If we were mid-table we would probably get on with it but we are fighting for our lives to retain our Premiership status and we owe it to our fans, we owe it to ourselves."
The FA is refusing to comment on the unprecedented case, but the rules do allow for clubs to take disputes to arbitration and if necessary to the Court of Arbitration for Sport.
It is not clear however whether the player's ban would be placed on hold until the case was dealt with.
Gold claimed most people would view the red card as wrong and that Carroll had been trying to shrug off Flores.
He added: "We are a club that understands there are rules and we abide by them. But you have every commentator and 80 per cent of the media saying it wasn't a sending off.
"Yet Howard Webb reviews the situation afterwards and says he stands by his judgement and when it goes to appeal and three guys stand by Howard Webb you feel 'how can this be right'.
"We are upset, we feel we have been badly treated.
"Most judgements are not made by three people, they are made by 12 - that's why they are called juries.
"I believe if you had gone to the FA Council and asked the 100 members 75 per cent would have said it was not a sending off, but if you just take three people it may not be representative."
Gold said Carroll's presence could be crucial for the rest of West Ham's season.
He said: "Of course it could. You can see the impact he has on our football club. I feel sorry for him as well - he was absolutely mortified.
"He was shrugging the guy off, okay he has messed his hair up but I don't think you should get sent off for messing somebody's hair up.
"There was a lovely tweet about Chico Flores saying he went to Vidal Sassoon and is now in intensive hair."