Wilkinson was booked for a mistimed tackle on Dembele in stoppage time of Stoke's Carling Cup win over Fulham on Tuesday night.
Cottagers boss Mark Hughes afterwards described the challenge as "absolutely ridiculous" and Stoke assistant Dave Kemp concured it was "unnecessary".
Pulis has now revealed his displeasure with Wilkinson over the tackle, but he is annoyed the post-match talk has surrounded the incident rather than the Potters' polished performance.
"I think the tackle was a little bit reckless," said Pulis. "It was a rash challenge but he's a young lad and desperate to show what he can do. But he's got to control that aggression.
"He plays with his heart and he's got the heart of a lion.
"He's not a bad lad and doesn't have any malice in him, but he has to play with his head sometimes because he didn't need to do it.
"Andy's got to learn and I'm sure he will. He's an intelligent lad and if he looks at it now he will say he shouldn't have done it.
"The disappointing thing is that we played so well and nobody talked about our performance, just about one incident."
Meanwhile Pulis has responded for the first time to Arsene Wenger's recent attack on Stoke in which he wrongly accused Ryan Shawcross of kicking Tottenham goalkeeper Huerelho Gomes.
"Arsene does what's best for Arsenal, and rightly so," Pulis added in the Stoke Sentinel. "Anybody who thinks any different is living on another planet. We all do the same.
"I don't care what other people say about my players or Stoke City, the only people I care about is our supporters and the chairman, Peter Coates."