Stoke City boss
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
He added: "There was a challenge in the first half in front of us,
"I went over to him and said 'well done, brilliant' - not only did he play exceptionally well but his behaviour was fabulous."
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 visitor 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.
"I am obviously disappointed we didn't win the game but I thought the attitude and application of the players was terrific.
"As the game on we got into good areas but it was just that final touch, that final decision at the end of it didn't allow us to score.
"There were a lot of real positives from the game and our first clean sheet which is important.
"We had so much dominance, particularly second half, so I was pleased with how we kept going."
Pulis insisted Stoke could have done even better after mistakes by Liverpool in the first half nearly gifted goals to
He said: "We are pleased, we have had three draws here in five years in the Premiership so we haven't done too bad.
"We just can't get that win that we would love. The first 20 to 25 minutes I thought we had the best chances and the best of the game and then they came into it and in the second half we had to defend resolutely.
"They worked their socks off, it's a good group, a very, very together group and we are pleased with the point."
Pulis confirmed that
Borussia Dortmund has confirmed Mario Gotze will miss the Champions League final against Bayern Munich at Wembley on Sunday (AEST).