Szczesny was shown a straight red card by referee Nicola Rizzoli for bringing down Arjen Robben of Bayern Munich in the penalty area in the Champions League last-16 tie at Emirates Stadium.
And, disgusted by the decision, the Poland international made an offensive hand gesture before he walked off down the tunnel.
Bayern's David Alaba missed the subsequent spot-kick but the German side went on to win 2-0 against the 10-man Gunners.
UEFA have yet to confirm whether Szczesny will face formal disciplinary charges over his gesture, but Wenger says the player will definitely be warned by his club.
"We will deal with that internally," he said. "We don't agree with that.
"Yes, it (the gesture) was frustration, but we are professionals, me included, and we have always to master reactions. Wojciech is part of that as well."
Lukasz Fabianski came on to replace Szczesny after the red card and the return leg at the Allianz Arena could be his final European appearance for the Gunners, if he is chosen to deputise again.
He is out of contract in the summer and 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."