Wenger shoved Mourinho and exchanged words with the Chelsea manager in the first half of Arsenal's 2-0 loss to their London rivals in the Premier League.
It came after Gary Cahill's reckless and dangerous challenge on Alexis Sanchez at Stamford Bridge.
Koscielny, in the France squad preparing for friendlies against Portugal and Armenia, said the Frenchman had lost control as his rivalry with Mourinho boiled over.
"It's a long history of friendship between the two coaches," he said.
"The facts are that after Cahill's tackle, I think the coach was a little upset because three days before Alexis Sanchez received the same tackle against Galatasaray. The player only got a yellow card.
"It's true, he [Wenger] flew out of control."
Koscielny gave away a first-half penalty against Chelsea, bringing down Eden Hazard as the Belgian surged into the area.
The 29-year-old joked he could be in the Guinness World Records books for number of penalties given away.
"It is true that I have conceded many penalties [seven since arriving in the Premier League]. I do not know if the Guinness Book of Records has that kind of record," Koscielny said.
"I have played about 200 games, and conceded eight penalties for Arsenal and the French team.
"If I could concede penalty kicks when the score is 4-0, it would be better for sure, but we don't choose.
"This weekend, there was a penalty. The situation must be judged early on. When Eden comes very quickly, he either scores or I clear the ball. It was toss of a coin."
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