Eden Hazard, with a first-half penalty, and Diego Costa, with his ninth goal in seven league games, struck as Wenger's bid for a first win against a Chelsea side managed by Mourinho goes on.
In 12 attempts the Frenchman is still to taste victory and his frustrations boiled over after Gary Cahill's tackle from behind on Alexis Sanchez in the 20th minute, when he pushed Mourinho in the chest as he strode towards the Chile forward.
Asked if he regretted the managers' long-running feud turning physical, Wenger said: "No
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."
Mourinho told the Frenchman to "back off" as the Gunners boss firmly planted two hands on the Portuguese's chest - risking Football Association disciplinary action - and the pair also eye-balled each other in close quarters.
"Honestly I don't listen to what he says," Wenger added.
"Look I trust you that you (the media) will teach me all the moral lessons over the next three weeks
And I can accept that."
Wenger admitted it was a push, saying "a little one".
He added: "I can try to push you
You can see when I really try to push."
The managers have a long history of conflict.
Mourinho on Friday refused to apologise for in February labelling Wenger "a specialist in failure" and their latest contretemps will have soured the relationship further.
The Chelsea boss preferred to move on.
Mourinho said: "Forget that (the push)
A football pitch is a football pitch, so no problem.
"It becomes heated because this is a big game, big clubs, big rivals, (an) important match for both teams
These conditions make a game of emotions.
"There are two technical areas, one for me, one for him
He was coming to my technical area and he was not coming for the right reasons.
"He was not coming to give some tactical instructions or something.
"He was coming to press the referee to give a red card and I didn't like that."
Mourinho praised Jonathan Moss for his handling of the incident, which saw referee Martin Atkinson warn both managers after consulting the fourth official.
The Blues boss, who did not speak to Wenger afterwards, declined to criticise his opposite number's conduct.
"To be fair, I do so many wrong things in football," Mourinho added.
"Sometimes you lose emotion and I did so many wrong things, but not this time, because this time I was just in my technical area and it was not my problem
Chelsea take a commanding advantage over second-placed Manchester City into the international break after dropping just two points in the opening seven games, in drawing 1-1 at the Etihad Stadium.
"The start of the season is good, but it's just seven matches and beginning of October," Mourinho said.
"We have only reasons to be happy
I feel the team is good in every moment of the game."
Thibaut Courtois had left for precautionary tests on a head injury in hospital before Hazard lit up the contest on the field, darting past two tackles before being felled by Laurent Koscielny for a penalty which he converted himself.
Mourinho said: "In these matches you need one of your top players to take some magic cards out of his pocket and he did it when the game was 0-0, when the game was tight."
Cesc Fabregas, playing against his former club, set up Costa's goal.
Mourinho said: "Fantastic (performance)
But to be fair he didn't have this performance because the opponent was Arsenal and he had a special motivation.
"He's been doing this since day one
I don't remember a game this season where he was not fantastic.
"To play against his team, the team where he was born or made for football, I think shows even more his commitment with us and his professionalism."
Wenger felt Fabregas handled a Jack Wilshere shot in the second half which should have been a penalty.
"It was a handball," Wenger said.
In a feisty encounter, Wenger also felt Cahill was fortunate not to be sent off for his challenge on Sanchez and bemoaned the persistent fouls he perceived were committed by Oscar and Branislav Ivanovic.
He also felt two instances of quality made the difference.
Wenger added: "It was a very even game today
It was down to very little
Hazard and Diego Costa made the difference.
"It was a very intense game
We couldn't score
Source : PA