Ashley Young was booked after he went down in the area under pressure from Kagisho Dikgacoi, with television replays showing that though there was contact, referee Jon Moss made the correct decision.
Moyes was disappointed to see a United player dive and admitted that he will be talking to the England international about his onfield conduct.
I've always said I don't like diving. He deserved to get booked, and even though the Palace player stuck his leg out, Ashley wrapped his leg around it, he told reporters after the match.
I don't want my players diving. You can see the boy definitely sticks his leg out so I'll be speaking to Ashley about it.
A penalty from Robin van Persie and a Wayne Rooney free kick secured the points for United, and the former Everton boss believes his side fully merited the victory.
We could have done with a few more goals but I thought we were dominant from the first whistle, Moyes continued.
Apart from the one opportunity I can't remember anything else that threatened us.
Overall I don't think the result was in any jeopardy. It just took a little bit of time to get the first goal.
Rooney, who played in a protective headband, put in a man of the match display on his return from a head injury, and Moyes was happy that the England man was able to complete 90 minutes.
