Pulis has labelled Suarez "an embarrassment" for his attempt to deceive the referee in the second half.
He told BBC Sport: "I've been on about and banging the drum about people who fall over and in one incident in the second half it's an embarrassment.
"The FA should be looking at this. Give him three games and he will stop falling over.
"Suarez is a fantastic player with great ability. 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."
A hard-fought point for Stoke keeps them above the Reds in the bottom half of the Premier League table going into the international break.