Moyes confirmed that he has spoken to United winger Ashley Young, who was booked for simulation during the 2-0 home victory over Crystal Palace on Saturday.
Young's booking has prompted much debate about the diving issue and Palace chairman Steve Parish thinks offenders should be sent off.
And Moyes, who has always been a stern critic of diving, says he has left Young in no doubt about his feelings on the subject.
But he also stressed that the diving incident had been dealt with correctly at the weekend by referee Jon Moss.
"I've had a word with him (Young) privately and, as I said after the game, I've said for many years we should have retrospective video for diving," said Moyes.
"I think that would help referees no end, as it's really difficult at times. It doesn't change my views, whether I'm at Everton or whether I'm at Manchester United.
"We can make up all the things we like about punishment but the rules are there and the referees have got the rules they have to abide by.
"The referee on Saturday did what he had to do, he gave him a yellow card.
"The referee got it correct and he gave the punishment for it, so I don't see why the debate should go on any longer."
Young was cautioned for simulation in the first half after deliberately tripping over Kagisho Dikgacoi's leg in a bid to win a penalty.
The England international won a spot-kick later in the game when he clashed with Dikgacoi, even though replays showed there was minimal contact between the two and the incident also occurred outside the box.
Dikgacoi saw red for what was deemed a professional foul by referee Jon Moss, but Palace supremo Parish thinks it should have been Young who received his marching orders instead.
"If preventing a goal-scoring opportunity is a straight red then trying to create one by cheating should be a straight red also," Parish said.
"The only player in the incidents that was honest was Kagisho Dikgacoi and he's sent off and banned for the next match.
"Ashley Young's dive and the appeal before put pressure on the ref to give a subsequent penalty that was certainly outside the area and probably wasn't even a foul.
"Ashley Young has a yellow card and three points and we have no points and one less player to pick from for the next game.
"(It) Might have cost us a point that might keep us up. (We) Need to get some momentum behind a straight red for a dive."
United manager Moyes warned Young after the match that diving would not be tolerated.
"I don't want my players diving. It's not what I want," Moyes said. "Dikgacoi definitely throws his leg out but Ashley put his leg into his leg."
Moyes' predecessor Sir Alex Ferguson also spoke to Young about his conduct after the former Watford man was accused of diving against QPR and Aston Villa.