The Scotland internationalist midfielder, who has had a chronic bowel complaint for almost three years, said he had always believed his playing days were not over.
"Other people around me were trying to make me think otherwise, but I stayed strong and believed I would get back," Fletcher said. "Playing a game like that, and getting an ovation like that, makes it all worthwhile."
His manager added: "If anybody returns from an illness to play professional football on this kind of stage for a club like Manchester United, it shows a lot about the boy himself. He has had to be on his own, he has been in and out of hospital, he has had operations.
"Today was a big message to a lot of people - keep believing. If you are not well then keep believing that you can get yourself right."
Alongside Fletcher's return, Manchester United's first win in three games - which came from Danny Welbeck's first-half brace and Tom Cleverley's first Barclays Premier League goal in nearly a year - pleased Moyes, although he called for more protection for Adnan Januzaj after accusing Aston Villa's players of queuing up to kick the 18-year-old winger.
"In every game, I don't know how many tackles there have been on him. That is why I am annoyed with fourth officials and referees. He is definitely not getting protected and before you know it the boy will get a sore one," said the Scot.
"It is terrible what they [the officials] are allowing to go on at the moment. They [opposition players] are queuing up to see who can kick him next. [Matthew] Lowton was booked but there were that many tackles on him from different players. It is a recurring theme and it's the referees' job to sort it out. You would hope they would recognise that."
Paul Lambert, the Aston Villa manager, rejected Moyes' interpretation, saying: "My team are not a physical team. We are a young side and maybe sometimes overexuberance gets the better of them but I have never sent anyone out to kick them."