Xhaka was removed as skipper earlier this week in response to his furious outburst at fans who jeered him during the draw with Crystal Palace a fortnight ago.
Wenger said, "As a manager you have to face these kind of decisions.
"We always face the unexpected as a manager, you have to make quick decisions.
"I think Arsenal Football Club is respected all over the world because it's built on values and everyone has to respect these values and the manager has to get them to be respected.
"Arsenal, for me, had always had a touch of class, for me football today in the modern era has a huge responsibility on the way we behave, the way were are examples.
"Arsenal are part of the big clubs in the world and we have to show that."
But Wenger continued a staunch defence of Xhaka when it was suggested to him that the Swiss international should not have reacted in that way.
"You can always but it doesn't mean in any club. It's not the motorway," he said. "You have people with passion, with the pressure they are under, with the disappointment they carry out, they have sometimes reactions you don't want.
"But you have to remind people of the behaviour you want.
"I think Xhaka is an intelligent player, contrary to what I heard in recent weeks.
"Finally he apologised and that's what he [Emery] wanted from him."