"I've been on about and banging the drum about people who fall over," said Pulis. "It's an embarrassment. The FA should be looking at this."
“I haven't seen the incident so I can't really comment on it but whatever Luis does there will always be a problem”
Brendan RodgersLiverpool manager
Pulis said a three-game ban would stop Suarez from "falling over."
However, the FA is unlikely to sanction the player, who went to ground in the Stoke penalty area despite no contact from an opposition player.
It only takes retrospective action against unseen red card offences and not offences that might have earned only a booking.
"Suarez is a fantastic player with great ability," added Pulis. "He is a handful and he is the one player we are frightened to death about.
"What happens is that he puts enormous pressure on the referee. Every time he goes down, you have got 40,000-odd Liverpool supporters getting after the referee and I don't think that's right. It is a tough enough job as it is."
Pulis also argued it is time for the Professional Footballers' Association to step in and address the subject.
Liverpool boss Brendan Rodgers preferred to praise Suarez's play rather than focus on that once moment in the game.
Rodgers praises courageous Liverpool
"I haven't seen the incident, so I can't really comment on it," said Rodgers, who has
complained to referees' chief Mike Riley
about some of the decisions against his side this season, including a lack of penalties in Suarez's favour.
"But whatever Luis does there will always be a problem, whether it's media, referees or whatever.
"It gets brought up every week, it's something that is not new. I thought he was terrific, some of his movement and combinations."
Rodgers was frustrated by the draw but praised his side, in particular his younger players, for the way they stood up to the physical challenge Stoke provided.
"They are a bunch of big men who make it difficult for you and there is no right or wrong way to play football," he added.
"What I was proud of is our young guys stood up to that. It was a physical game but no complaints from us.
"I am obviously disappointed we didn't win the game, but I thought the attitude and application of the players was terrific."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.