After the Hammers had taken the lead through Mohamed Diame, Nolan saw a point-blank header turned away by David Stockdale.
But that was as good as it got for West Ham and Nolan. Steve Sidwell headed home an equaliser before Nolan was then sent off for kicking Fernando Amorebieta off the ball.
With the extra man Fulham went on to dominate and it was little surprise when Dimitar Berbatov sealed their win just after the hour.
And Allardyce admits Nolan's sending off was crucial.
"Our captain was irresponsible today - not just today but for the future because he's suspended," said Allardyce, who is even more disappointed given Nolan was red carded only last month for a stamp on Liverpool's Jordan Henderson.
"I just don't quite understand why he's lost his cool. He's probably responsible for us losing the game more than anybody else, I don't think there's any doubt about that.
"I don't understand it because the indiscretion of what he's done has just happened straight after what he did at Liverpool.
"So I'm going to have to find out what's wrong with him, because there's certainly something wrong with his mentality at the minute.
"At his age and with his experience, and over the many years I've known him, I've not seen this type of reaction or this type of situation he's put himself into."
Allardyce admits that West Ham's squad is struggling to cope, and his troubles were added to by an injury to Mark Noble.
"We have very great difficulties at the moment coping with the injuries we have," he said.
"The way we started was fine - nice and compact in very difficult conditions and two teams feeling the strain and we got the goal.
"But the two turning points was the Kevin Nolan header which would have made it 2-0 and then getting himself sent off which is very irresponsible to say the least."