The United winger 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 was deemed a professional foul by referee Jon Moss, but 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 told BBC Radio 5 Live.
"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 David 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.
- Sports & Recreation
- Ashley Young
- Kagisho Dikgacoi
- Manchester United