"When dealing with managers of that esteem, people sometimes take their word as being honest and perceive you to be something that you're not.
"That has got to be addressed."
Wenger condemned Shawcross and Rory Delap after Adebayor and Theo Walcott were injured in Stoke's 2-1 victory at the Britannia Stadium.
Both Adebayor and Walcott were stretchered off during Saturday's game after coming under challenges from Shawcross and Delap respectively.
Adebayor has subsequently been ruled out for three weeks, while Walcott is doubtful for Arsenal's game against Manchester United.
"We've got Mike Riley on Saturday and it will be interesting to see how he referees the football game and whether he goes on the perception of what Wenger says or whether he goes on what he sees," Pulis told BBC Radio 5 Live.
"People in general can be swayed if they're not watching you play and seeing what you are trying to achieve. They read the papers and unfortunately a lot of people believe what they read."
In an interview with BBC Radio Stoke, Pulis added: "The last thing I want is people to have a perception about us that is not true.
"I don't want us branded as a dirty team. We are a competitive team but we are not a dirty team. We played Manchester City away two weeks ago and didn't have one booking.
"It's moved the spotlight away from their bad performance. I think we've come out quite well in this."
At a Champions League news conference on Tuesday, Wenger questioned: "Do you think Delap tried to play the ball when he tackled Walcott? Or that Shawcross tried to play the ball when he tackled Adebayor off the pitch?"
But in a statement published on the club's website Pulis leapt to the defence of his players, and reminded Wenger that Robin van Persie was dismissed for striking Stoke goalkeeper Thomas Sorensen.
Midfielder Delap has also protested his own innocence over the incident that caused England international Walcott to leave the field with his arm in a sling.
He told BBC Radio Stoke: "It was a tired tackle. I was trying to get the ball but he was too quick for me.
"I wish him all the best and I will try and get to see him."
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