Eden Hazard's first-half penalty and Diego Costa's ninth goal of the season saw the hosts to victory in a fiery Premier League encounter at Stamford Bridge.
Laurent Koscielny, Calum Chambers and Danny Welbeck were all arguably fortunate not to be given their marching orders by referee Martin Atkinson, while Gary Cahill's aggressive challenge on Alexis Sanchez sparked an altercation between the two managers on the touchline during the opening period.
Wenger entered Mourinho's technical area and laid his hands on the Portuguese's chest, before Atkinson called both coaches over to calm tempers.
The Frenchman explained his actions in a post-match press conference, and was unequivocal in his response when asked if he regretted the incident.
"No," he said. "What is to regret after that?
"I wanted to go from A to B and somebody confronted me in between without any sign of welcome.
"B was Sanchez, to see how badly he was injured. Honestly, I don't listen to what he [Mourinho] says."
Wenger conceded that he had pushed Mourinho "a little", and felt some of Chelsea's players were perhaps fortunate not to be sent off.
"I think Oscar was lucky to stay on the pitch with the repeated fouls he made," said Wenger.
"He got a yellow card in the 88th minute and he was purposefully fouling on every break. [Branislav] Ivanovic as well, there were some bad fouls but that's down to the referee, it's not down to me."
Defeat means Arsenal's unbeaten start to the league campaign has come to an end, but Wenger felt there was little to choose between his side and Chelsea.
"It was down to the little things that were on their side but it was a very even game," he said.
"If you look at the number of saves our keeper had made you find nothing, and theirs as well, so the game was about who can take advantage of an opportunity.
"We couldn't score and they did so at the end of the day you have to say yes [Chelsea were more ruthless]."
