Pulis was incensed by a blatant dive by Suarez toward the end of the game and again demanded the issue of simulation be looked at.
He told BBC Sport: "I thought Suarez again today...I've been on about people falling over and the one incident in the second half...it's an embarrassment being a professional footballer (and doing that)."
Pulis added: "He's a fantastic player, he's got great ability and he is the one player we were frightened to death of today, but doing things like that. Retrospective decisions are made on a Monday by the FA and they should be looking at this. Give him three games and he will stop falling over.
"What happens is that he puts pressure on the referee and every time he goes down you've got 40,000 Liverpool fans getting after the ref and I don't think that's right. I don't know how many times he has fallen over but the one in the penalty box is just an embarrassment and how he has not been booked I just don't know.
"I am concerned about the simulation and putting pressure on the ref. It's a tough enough job as it is. For professional footballers to be doing that is just not right and the PFA should start talking about it."
Liverpool manager Brendan Rodgers insisted he had not seen the Suarez incident but defended his player.
Rodgers said: "I haven't seen the incident so I can't really comment on it, 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 today, some of his movement and combinations."
Rodgers admitted to being frustrated by the result, but was full of praise for his players for standing up to a physical Stoke side, but he did not believe the visitors had been over-physical.
He added: "No, they are a bunch of big men who make it difficult for you and there is no right or wrong way to play football. What I was proud of is our young guys stood up to that. It was a physical game today but no complaints from us. I thought maybe the referee didn't see it that way and didn't give some decisions he should have done."
- Sports & Recreation