West Ham were forced to hang on for the final 15 minutes after Aaron Cresswell was controversially shown two yellow cards in quick succession, but Noble was pleased with how his side responded to the setback.
"Obviously going down to 10 men seemed like an hour to play but the boys at the back, the whole team, defended well," he told BT Sport.
"I've been the first to criticise the team and the way we have played, I involved myself in that, but tonight we showed how much it means to us to put a win on the board.
"After the amount of games we've played you don't want to keep talking about injuries, especially wing-backs like Cress, who are so important in this day and age. We are going to miss him next week now. Those three points were massive for everyone who works at the club."
Palace missed a penalty and struck the woodwork on their way to the defeat.