Pulis almost had to be dragged away from the fourth official when Barton went down on the edge of the Stoke penalty area - then bounced up when Newcastle created another attack.
Tony Pulis: "With the bad publicity we have had this week with the challenge from Andy Wilkinson, I was really disappointed when one of the Newcastle players went down and I think simulated an injury from a challenge.
"Three passes later, he jumped up and was running around as if nothing had happened.
"The PFA have a responsibility as an organisation to make sure their players don't do things like that because you put other players under enormous pressure, but also you but referees and officials under enormous pressure.
"We have been highlighted with one or two other clubs for supposedly being over-physical, and there are other aspects to our game that need to be addressed, and that is certainly, for me, one of them.
"I don't know (who the player was), you will have to look at the tape yourself."