The Poland international was shown a red card by Italian referee Nicola Rizzoli after tripping Arjen Robben in the box and made an obscene gesture before heading off down the tunnel.
UEFA is yet to confirm whether the matter will lead to any formal disciplinary charges, but Gunners boss Wenger confirmed the club would remind the player of his responsibilities.
Speaking ahead of Saturday's Barclays Premier League game against Sunderland, Wenger said: "We will deal with that internally. We don't agree with that.
"Yes, (the gesture) was frustration, but we are professionals, me included, and we have always to master reactions. Wojciech is part of that as well."
Although their resultant penalty was also missed, Bayern finally broke the deadlock in the second half with goals from Toni Kroos and Thomas Muller which all but ended Arsenal's European ambitions for another season.
Lukasz Fabianski, who replaced Szczesny on Wednesday night, is out of contract in the summer and so next month's clash at the Allianz Arena could present his last European appearance for the Gunners.
Wenger said: "Fabianski, of course it is a possibility that it is his last campaign with us. He wants to play somewhere, but if he changes his mind, my door is open."