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).
"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."
Pulis contrasted Suarez's dive with Glen Johnson's reaction to a strong Stoke challenge.
He added: "There was a challenge in the first half in front of us, Jon Walters and Glen Johnson both went up for a header, it was a proper old-fashioned challenge.
"Glen Johnson did absolutely fantastic, just bounced back up on got with the game, it was a proper, proper challenge.
"I went over to him and said 'well done, brilliant' - not only did he play exceptionally well but his behaviour was fabulous."