"I think one day football will have to tackle that," said Wenger. "It's easy to sit in the stand and insult people. It's the easiest sport in the world.
"I'm not responsible for the way people behave in the stands. If you want to stop that, it's easy to stop. You can isolate every single face."
Robin van Persie equalised for the Gunners after Peter Crouch put the home side ahead, but matters on the field were not the only things occupying Wenger's thoughts after the game.
He added: "I think sometimes when I go out on the pitch at the end of the game and people are angry or hateful, I would like a little picture to send home for them to show their son or daughter, and then come back next week and see if they will do it again, see if they are proud of you."
A feisty rivalry has developed between Arsenal and Stoke in recent years and there were also some jeers directed at Arsenal midfielder Aaron Ramsey.
Pulis salutes Stoke 'spirit'
Ramsey broke his leg in a game at Stoke following a tackle by Potters defender Ryan Shawcross in February 2010, and the centre-back has since been the subject of abuse from some Arsenal fans.
"I don't think you can be especially proud to boo Aaron Ramsey, I don't see what he has done wrong," said Wenger.
"It's an old story where the fans of Stoke stand behind their player but it shouldn't go as far as booing Ramsey."
Stoke manager Pulis refused to criticise his club's supporters but accepted there is a problem regarding abuse from the stands.
"It is very difficult for us all," he said. "I go to grounds and get abused.
"It's not just Arsene. If you speak to Sir Alex [Ferguson], he gets absolutely slaughtered at some grounds. Is it acceptable? The powers-that-be have got to decide that."
On the boos aimed at Ramsey, he added: "I was more concerned about the Arsenal supporters booing Shawcross so I didn't hear the ones on Ramsey." Stoke City's run-in
The point leaves Arsenal third in the Premier League and they can secure a top-three spot and certain qualification for the Champions League with wins from their last two games against Norwich and West Brom.
"It was a game where we showed great character and great battling qualities," said Wenger, who felt his side should have been awarded a penalty for a Glenn Whelan challenge on Yossi Benayoun.
"It was a game of two different approaches. One very direct and one who tries to play on the ground, and both teams are good at what they do.
"We had good chances, especially in the first half. I felt in the second half our fluency dropped a bit but we still had some chances, especially the penalty that wasn't given.
"Overall we deserved at least a point and I can only give credit to my players. We have not always coped with Stoke's play, but [this time] I felt we did." Also related to this story