Down 2-1 deep into stoppage time, West Ham won a penalty thanks to a handball from Luke Shaw.
But David De Gea stepped up to save Noble's penalty to secure all three points from the Red Devils.
Moyes said: "Do I regret it? Not at all because Mark Noble is one of the best penalty takers we have got.
"We had time to think about it, time to make that choice. My choice, my decision.
"You have to make big decisions. Sometimes they go and sometimes they don't. I think I would have been more disappointed in myself if I hadn't made the decision."
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