The pair needed to be separated by fourth official Howard Webb after City boss Mancini took exception to Moyes picking up the ball - an action the Italian interpreted as time-wasting.
The incident ended with both being sent to the dressing rooms for the closing moments by referee Peter Walton.
Although both managers played down the incident afterwards and apologised to each other in the tunnel, they could yet face a misconduct charge, resulting in a possible touchline ban, from the Football Association.
Arsenal manager Wenger is no stranger to clashes in the technical area, having confronted both Tottenham manager Martin Jol and West Ham boss Alan Pardew in recent seasons.
The Frenchman, however, insists such flashpoints are understandable when passions run high, with so much at stake.
Wenger said: "I had some [incidents], but we are all under pressure.
"During a game at one specific moment it can happen that, for a fraction of a second, we lose it a little bit.
"It can happen to anybody.
"Even if after the game, 'come on let's behave properly' it can still happen.
"It just shows that we are humans like everybody and that we care."
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