The 31-year-old's second red card in four matches helped condemn the Hammers to a big defeat at the bottom, with the manager left bitterly disappointed with his captain
The 31-year-old was sent off for kicking out at Cottagers defender Fernando Amorebieta just before half-time, with the score at 1-1, before the hosts went on to win 2-1 after dominating the second half.
After the match Allardyce made no excuses for Nolan and suggested that the Englishman's dismissal was the main reason behind the New Year's Day defeat.
"I don't think there's a problem with the sending off - it's Kevin's reaction," the 59-year-old told reporters. "The disappointment of that reaction and the disappointment of getting sent off is obviously massively costly for us today.
"I don't understand why he's lost his cool. I know the centre-half has obstructed him, jumped in front of him and fouled him. Mark Clattenburg didn't give a free-kick, which he should have done, but it's still not an excuse for what Kevin did.
"When you get a man sent off and you lose one player it gets very, very difficult indeed. So [Nolan's] responsible for, probably, us losing the game more than anyone else - I don't think there's any doubt about that."
The dismissal comes soon after Nolan's return from another four-match ban for a straight red against Liverpool - something that is making Allardyce question his player's mentality.
"I don't understand it because the indiscretion of what he's done has happened straight after what he did at Liverpool," he added. "I'm going to have to find out what's wrong with him, becuase there is certainly something wrong with his mentality at the minute.
"The responsibility of a player is to play the game the best he possibly can, to go out and be disciplined, and to go out and apply his talents within the rules of the game - not to lose your cool, not to lose your head and not to do anything silly.
"You can expect it from somebody who's starting out occasionally, as a youngster in the game that all of a sudden finds out the nitty gritty that happens in the Premier League - but not Kevin."
When asked whether he would rethink Nolan's captaincy, Allardyce replied: "I don't know yet. I'm disappointed enough with what he's done and time will tell. We'll deal with the situation internally.
"My thoughts are now with the players who are available for playing, and not with Kevin Nolan who isn't available. Today I think we would have certainly got a result had Kevin not been as irresponsible as he was."
Fulham boss Rene Meulensteen, meanwhile, was pleased with his side's victory and revealed his two new assistants Ray Wilkins and Alan Curbishley - both present on the bench on Wednesday - were and will continue to be involved in tactical decisions.
"That's what you want from a number two, and the same with Alan Curbishley," he said. "It's very important that you've got the right team and people around you. I'm delighted that both Alan and Ray have decided to join us."