The 28-year-old was cautioned for simulation after a clash with Crystal Palace defender Kagisho Dikagacoi before the United star went on to win the Red Devils a penalty on the stroke of half-time in the 2-0 victory.
Young has previously picked up a number of yellow cards for diving following his big-money move to United in 2011, and Moyes confirmed he has had a private word with the England international about the incident on Saturday.
“I can never be sure that it won’t happen again. I’ve had a word privately,” Moyes said.
“I have always said that it is something we should have retrospective video action for. That would help the referees no end. It is really difficult for referees.”
Palace chairman Steve Parish has called for players to receive a red card if referees deem them guilty of simulation, while former Premier League official Graham Poll wants to see automatic five-match bans for diving.
Moyes added: “We can make up all the things we like for punishments but referees have rules that they have to abide by and the referee on Saturday did what he had to do and gave him a yellow card.
“My views on this don’t change from being Everton manager to Manchester Utd. The referee got the decision correct and called it right. He gave him the punishment.”