Young was cautioned by referee Jon Moss after going to ground following a tackle by Kagisho Dikgacoi, with replays suggesting he had made the most of the incident.
The England international was later awarded a controversial penalty after tangling with Dikgacoi once again, with the Palace man dismissed by Moss.
"I don't want my players diving," said Moyes, when asked about the yellow card. "I don't want anybody doing it.
"The boy (Dikgacoi) definitely throws his leg out but I think Ashley has put his leg into his leg. It is not what I want."
Robin van Persie opened the scoring from the spot after Dikgacoi's dismissal, with Moyes admitting Palace could feel hard done to.
"I don't like the rule where every time it is the last man it means it is (a red card)," said Moyes. "I thought it was harsh. If I was Ian Holloway I would be disappointed.
"OK, it might be a penalty. But I don't think the boy made a challenge to wipe him out. Unfortunately that is the rule."
United did not impose themselves in the manner Palace boss Ian Holloway feared and it took a late free-kick from Wayne Rooney to seal the points.
Rooney was only a confirmed starter on Friday evening after he had tried out a strange looking cushioned head guard to protect the area where he had 10 stitches following a training ground collision with Phil Jones.
"It was a difficult decision," said Moyes. "We got the headband on Friday and we wanted to see how he felt with it. If I thought he could wear it I would try and get him out.
"He tired a little bit in the second half but I wanted to get the 90 minutes out of him because he lacks match practice. It helped him towards the overall goal of getting him match sharp."
Moyes was also able to introduce £27.5million new-boy Marouane Fellaini for his debut, although the Belgian was overshadowed by fellow countryman Adnan Januzaj.
The 18-year-old unsettled the Palace defence more than any other United player and won the free-kick from which Rooney scored his first goal since March.
"I considered playing him from the start," said Moyes. "His performance when he came on showed it would have been merited.
"He didn't look fazed and did a lot of good things. He moved the ball well. He is going to be a good player."