The managerial rivals clashed during the first half of Chelsea's 2-0 win at Stamford Bridge in the Premier League, with Wenger laying his hands on the Portuguese's chest.
The spat was sparked by Gary Cahill's forceful challenge on Alexis Sanchez, which Wenger felt deserved a red card.
Referee Martin Atkinson showed only a caution to the England international defender and the official then called Mourinho and Wenger over following the fracas in an attempt to calm tempers.
The pair did not shake hands at full-time and Mourinho, who is yet to lose to Wenger in 12 previous meetings between the pair, seemed unfazed by the incident.
"For me it's over but the technical area is very clear," he told Sky Sports.
"I have mine and he has his, he cannot come to my technical area to put pressure on the referee to give cards to my players, so I told him to leave my technical area and don't come back please, no problem."
Although Cahill was perhaps fortunate to remain on the field, Arsenal could have seen their numbers depleted.
Laurent Koscielny could have been shown a straight red card for his foul on Eden Hazard that allowed the Belgian to open the scoring from the penalty spot, while Calum Chambers was perhaps lucky to not receive a second yellow for a tug on Andre Schurrle. And Danny Welbeck's two-footed lunge on Cesc Fabregas in the final moments received only a caution from Atkinson.
"I think the referee by the technical point of view had a fantastic performance in a difficult match," Mourinho said.
"I think they did a fantastic job because it's a red card on Koscielny and a double yellow card on Chambers.
"A clear red card on Welbeck but I accept that one, the game is over, he's a good kid and not aggressive. Maybe it was just a reaction of the frustration."
After Hazard's penalty, Diego Costa's ninth goal of the season 12 minutes from time ensured Chelsea moved five points clear at the top of the Premier League, while Arsenal's unbeaten start to the league campaign came to an end.
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