The Uruguayan forward appeared to go down under minimal contact in an incident in the second half in Sunday's 0-0 draw at Anfield, and made a theatrical attempt to try and win a penalty - something the Potters manager wants the FA to take action against.
"Retrospective decisions are made on a Monday and Luis Suarez should be punished," Pulis told reporters. "The one in the penalty box was an embarrassment and how he wasn't booked I don't know."
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Suarez has been at the centre of diving controversy in recent weeks, with his manager and Liverpool team-mates insisting that his reputation for diving goes against him in many incidents.
"I haven't seen the incident so I can't really comment," Rodgers said. "But whatever Luis does there will always be a problem.
"It gets brought up every week whether it's with the media or the refs, but I thought he was terrific today."