Noble came off the bench for the Hammers to take the penalty that had been awarded after a Luke Shaw handball, but De Gea made a smart stop to help his side record a 2-1 victory in the Premier League affair.
The Spain international said that it was "a massive three points" for the 20-time English champions, while he also paid tribute to Jesse Lingard, who scored the winner against the side that he represented on loan last term.
"It was the last minute, I made the save. A massive three points for us. Going through my head was 'save the ball'. It was a really tough game, both teams had good chances, again a great goal from Jesse," De Gea told Sky Sports News.
"It is a massive three points. In the dressing room we said the three points were the most important thing."
Lingard then came off the bench to net an 89th-minute winner against David Moyes's side.