Stoke hosted the Gunners at the Britannia Stadium in the Barclays Premier League on Sunday in an edgy goalless draw with home fans jeering Arsenal players and manager Arsene Wenger.
The animosity dates back to an incident two and a half years ago when Arsenal's Aaron Ramsey's leg was badly broken in a tackle from Stoke's Ryan Shawcross, and the mood was evident on Sunday as both sides went in search of their first league win of the season.
Pulis admitted the matter is out of his control.
"Irrespective of what I say or what Arsene says, you can't affect what people do," said the Potters boss.
"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."
Next up for Stoke is the cup clash with npower League One new boys Swindon, and Pulis has no new injury worries to be concerned about.
The Potters boss could rest several players following Sunday's draw against Arsenal and bring in the likes of Wilson Palacios and Dean Whitehead, who is back from a one-game suspension.
American Geoff Cameron, who played at the weekend despite having only just arrived in the country, is likely to sit out.