Stockdale made a fine stop to deny Nolan with West Ham already 1-0 up at Craven Cottage.
Steve Sidwell subsequently equalised for Fulham and Nolan was then sent off prior to Dimitar Berbatov's winner, which moved Rene Meulensteen's side out of the Premier League relegation zone.
"I wouldn't say my save was pivotal," Stockdale told Fulham's official website.
"I'd say the second goal was pivotal as it won us the game. I'm just doing my job and if I can keep the lads in the game, then so be it.
"It's not until afterwards that you think about it; at the time you just want the three points.
"We're in a relegation battle and we won't get out of it by sitting back and looking at individual performances - we have to play as a team.
"You saw the character we possess to come from 1-0 down. We had a little bit of help with the sending off but even at 1-0 we had chances to get back into it."
Victory over West Ham was particularly welcome for Fulham given the 6-0 loss they suffered at Hull City four days earlier.
"We thought it was such a freak result at Hull that we couldn't dwell on it," Stockdale added.
"If we'd lost 1-0 in the last minute we might have thought about it more.
"You can't think about results too much – we can't think about West Ham really now as we need to get back on the training pitch ahead of an FA Cup game at Norwich City that we want to win.
"But we're delighted to get six points out of a possible nine over the festive period. We've now got to use these two victories to push on and get up that table."
