Arsenal had a dreadful record away to the Potters during Wenger's tenure, losing there five times in the Premier League and once in the FA Cup.
Pulis told the BBC's That Peter Crouch Podcast: "I always want angles to get players motivated, to put fire into their bellies and something for the supporters to feed off.
"When Wenger first said it, called us a rugby team, it was the third time on the bounce we had beaten them at home.
"He was avoiding the question of how could a team with much less talent than Arsenal, who don't spend anywhere near as much as Arsenal, who haven't got the facilities and capabilities of Arsenal, keep beating Arsenal.
"Patrick Vieira told me, 'We used to hate going to Stoke. You were the only club that Wenger actually talked about and worked on before. We just couldn't beat you'.
"Wenger came one year and complained about the grass being too long. He wrote a letter to the FA. The referees and the linesman had to come and measure the grass.
"I know he talked about banning throw-ins and saying they shouldn't be allowed. That was all music to our ears."