Noble was given his marching orders for a second bookable offence five minutes after giving West Ham a 2-1 lead from the penalty spot, and Allardyce was convinced that the decision was a turning point in the game.
Everton went on to snatch the points as two Leighton Baines free-kicks were added to by a late winner from substitute Romelu Lukaku, and the West Ham manager insisted that the official got a key call wrong.
"I've had a look at it and it's easy for me to say that he (Noble) got the ball but he did because I can see it on the laptop, the referee sees it from where he is but he's got to be certain," Allardyce said.
"Baines might have put the free-kick in but we would have still been 2-2 with 11 men not 10."
Despite the result, Allardyce stressed that he was more than satisfied with his team's first-half performance.
He continued: "We were playing against a very good side and I think we matched them and the goal from Ravel (Morrison) was great.
"It gives him a lot of confidence in his development and the growth he's got but we found the difference in Everton when Lukaku came on.
"We had to make sure we controlled that situation, which was Everton getting more and more in the attacking mode, because playing off him was more difficult for us to cope with. But our defensive qualities really shone through again.
"I thought 'If a few do our defensive job like we normally do then we'll be okay today now and we'll probably get the win'. And then the game changes, and none more so than the Mark Noble sending off."
