The former Everton manager had a quiet word with England winger Ashley Young following two controversial incidents during Saturday's 2-0 victory against 10-man Crystal Palace
Young received criticism following two incidents with Palace midfielder Kagisho Dikgacoi, the latter of which saw the South African sent off and concede a penalty on the stroke of half-time.
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"I've had a word with him [Young] privately and I said after the game, I've said for many years - I think we should have retrospective video for diving. I think that would help referees no end. It's really difficult at times," Moyes told reporters.
"It doesn't change my views whether it's at Everton or Manchester United. We can make up all the things we like about punishment but the rules are there. The referees have got the rules they have to abide by and the referee on Saturday did what he had to do - give him a yellow card."
Moyes admits he is worried about his side’s lack of goals from open play after Robin van Persie and Wayne Rooney both scored from set-pieces against Palace, following two blanks against Chelsea and Liverpool.
"It's a little bit of a concern because we've played well and had a lot of attacking entries into opposition penalty areas," he said. "If we're winning without having to score too readily then that's great."
United take on Bayer Leverkusen in the Champions League on Tuesday night, which will give Moyes his debut in the competition's group stages after his Everton side were eliminated in the qualifiers for the 2005-06 edition.
"I'm really excited about it," he added. "I was excited at joining Manchester United. Every game's offered a new challenge, a tough one at that as well and I'm really looking forward to the Champions League.
"I've been there before with Everton, we played Villarreal, we didn't quite make the group stages but this is something different. I'm now managing a club that is used to getting close to the final stages and hopefully we'll try and do that again."