The Manchester United winger was booked for simulation before earning a penalty after another controversial incident with Kagisho Dikgacoi at Old Trafford
Young received a caution after feigning a challenge from Kagisho Dikgacoi before a second tackle between the two players resulted in a penalty being awarded for United and the Palace midfielder being dismissed.
Robin van Persie converted the spot kick as United secured a 2-0 victory over Ian Holloway's side.
"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."