The bad feeling between the two clubs dates back to when Stoke defender Ryan Shawcross broke Arsenal's Aaron Ramsey's leg in a tackle two-and-a-half years ago, a challenge that the Gunners boss Arsene Wenger described as "horrendous" and "unacceptable".
The two sides met again in a 0-0 draw at the Britannia Stadium yesterday, with Wenger and his Arsenal players being jeered by the home support. Pulis, however, believes that the animosity is beyond his control.
"Irrespective of what I say or what Arsene says, you can't affect what people do," the Potters boss said.
"As I've said, if I can't affect it I don't worry about it and I personally don't think I can affect it. That's got to be other people doing that not me and that's got to be something that happens outside my sphere.
"You can say and I've said it before. That's gone. We've moved on."
Stoke's next match comes tomorrow night as they face Swindon in the League Cup.