The 23-year-old Spain shot-stopper has only kept four clean sheets in the Premier League so far this season as the champions have struggled to keep opponents at bay.
However, De Gea has also made several outstanding saves, particularly in recent weeks, and needed to be at his best to keep out James Chester in the closing moments of United's 3-2 Boxing Day win at Hull.
Moyes believes the former Atletico Madrid keeper, who endured a shaky start in Manchester, is among a clutch of United stars who will be around at Old Trafford for a long time to come.
The Red Devils boss said: "He is one of five or six young players in the team who are going to be part of the next five or six years and that means he can only get better.
"The defenders have always trusted him because they knew the potential for him to get better was there."
Moyes knows much of the focus is on his star names Wayne Rooney and Robin van Persie but like Peter Schmeichel in the past, the role of the goalkeeper is crucial to United's success.
"Wayne and Robin score big goals and win games for us - but David has won us big points as well," Moyes added in The Sun.
"His save at Sunderland comes to mind and he did it again at Hull.
"He is also coming and taking crosses and being brave and we want him to do that.
"One of the hardest things to do is put a young goalkeeper in. He made a few mistakes but Sir Alex (Ferguson) stuck with him.
"He really trusted him and believed in him and we are seeing the fruits of that.
"He is now turning into a man and getting stronger and looking at the top of his game.
"He is getting used to the Premier League and understanding what he has to do, he is coming and catching and taking things, sometimes that is what you have to do, you have to be brave. He is punching well too."