Manchester United manager David Moyes has called for retrospective action to help punish players who dive.
Ashley Young was booked for tumbling over in United's 2-0 win over Crystal Palace at Old Trafford on Saturday.
"I have said for many years diving is something we should have retrospective video for. That would help referees no end," said Moyes.
Palace chairman Steve Parish wants players who dive to be shown straight red cards following the incident.
Moyes added: "You can never be sure it won't happen again but I have had a word with him (Young) privately.
"It is really difficult at times. Moving from Everton to Manchester United doesn't change my views on that."
Young's caution came after he was challenged by Palace's Kagisho Dikgacoi, who was later sent off by referee Jon Moss for a foul on Young that resulted in a penalty, from which United took the lead.
"If preventing a goal-scoring opportunity is a straight red then trying to create one by cheating should be a straight red also," said Parish in an email to BBC Radio 5 live's 606 programme on Sunday night.
"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.
"Might have cost us a point that might keep us up. Need to get some momentum behind a straight red for a dive."
The Football Association says that any changes to the rules regarding all issues, including simulation, would come from Fifa, the game's world governing body.
It added that it regularly discusses all matters, including simulation, with bodies including the Premier League, the Football League and the Professional Game Match Officials Limited refereeing body.
In July, the FA made a change to its process on retrospective action to strengthen its powers to deal with violent incidents.
The move was made after Wigan's Callum McManaman escaped censure for a dangerous tackle in a Premier League game against Newcastle in March - because an official saw the incident at the time.
Following the amendment, the FA can take retrospective action where officials might have seen an incident of violent conduct but were not in a position to assess it fully.
But there is no suggestion that the FA is seeking to alter how it deals with incidents of simulation.
In 2009, Uefa banned Eduardo of Arsenal retrospectively after he appeared to dive to win a penalty under a challenge from Celtic goalkeeper Artur Boruc during a Champions League qualifier but that was later overturned.
Fifa allows some room for individual associations to make their own decisions within the game if appropriate, and the Scottish FA assesses simulation incidents retrospectively at tribunals.
Last season, 34 yellow cards were shown for simulation in the Premier League, up 14 on the previous season's total and the highest recorded over the previous four years.