The tussle was broken up by fourth official Jonathan Moss, and although Wenger has admitted that he "regrets" some of his actions, he has insisted that Mourinho is to blame for the coming together.
"In hindsight I think I should not have reacted at all, it's not a way to behave on a football field," Wenger is quoted as saying by the Metro.
"I always regret any signs of violence and I apologise, but that's a part of games where everything is manic. And then we have quite a substantial past.
"Did Mourinho provoke me? That is how I felt. I did not enter Chelsea's technical area."
The loss was Arsenal's first in the league this season, but they have only won two of their seven games so far and lie in eighth place.