Young was booked for diving during the 2-0 win over Crystal Palace, sparking a huge debate in which Eagles chairman Steve Parish claimed offenders should be sent off.
A long-time critic of divers, Moyes admitted he cannot be completely certain it will never happen again. But he has left Young in no doubt about his feelings.
"You can never be sure it won't happen again but I have had a word with him privately," said Moyes.
"I said after the game and I have said for many years diving is something we should have retrospective video for. That would help referees no end.
"It is really difficult at times. Moving from Everton to Manchester United doesn't change my views on that."
Not that Moyes felt referee Jon Moss got his decision wrong at the weekend.
"The referee got it correct," said Moyes. "He gave the punishment for it so I don't see why the debate should go on any longer."
The United boss confirmed Wayne Rooney will require the headband he wore during Saturday's game should he feature in Tuesday night's Champions League encounter with Bayer Leverkusen even though he trained without it on Monday morning.
It will be Moyes' first group game in the competition, having been beaten by Villarreal in 2005 in a final qualifying round tie with Everton.