With the Hammers trailing 2-1, club captain Noble, their Mr Reliable from the spot, was summoned from the bench by Moyes to take the penalty after Luke Shaw handled in the area.
Noble had not missed a penalty since December 2016, remarkably eight months after De Gea last saved one – some 40 spot-kicks ago.
But the long-serving midfielder, who retires at the end of the season, was denied his moment of glory when De Gea dived to his left to claw out his effort.
Sky Sports pundits Roy Keane and Graeme Souness criticised the decision, saying the player was neither warmed up nor up to speed with the game.
But Moyes insisted: “Do I regret it? Not at all.
“That’s what happens in management, you have to make big decisions. Sometimes they go for you, sometimes they don’t.
“I just thought, we have a really good penalty taker on the bench. I’d have been more disappointed if I hadn’t made the decision. If one of the other players had taken it and missed I’d have thought, ‘Why didn’t I bring Mark Noble on’?
“He has an incredibly good record on penalties. So with Mark going on, and De Gea not saving many, I’m hoping that is the equaliser.”
Even United boss Ole Gunnar Solskjaer feared the worst when he saw Noble come on.
“I’ve seen Noble score so many penalties, so you feel down and out and expect to come home with a point,” he said. “But luckily David has continued his fine form.”
West Ham had taken the lead through Said Benrahma’s deflected strike, but Cristiano Ronaldo’s fourth goal in three matches sent United in at half-time level at 1-1.
Solskjaer felt Ronaldo was denied two clear penalties when he tumbled under challenges from Vladimir Coufal and Kurt Zouma.
“Of course we’re very happy with the win and I felt we deserved it,” he added.
“We played some good football and created some good chances and Cristiano should have had two penalties, but luckily David saved that penalty at the end.
“Jesse wants to fight for his place and for me he’s really contributing. I’m pleased for him.”