For the second successive season Arsenal face a two-goal first-leg deficit when they head to the Allianz Arena after Toni Kroos and Thomas Muller scored at the Emirates Stadium.
Had Mesut Ozil scored an early penalty things might have been different and there was a temporary reprieve when David Alaba also failed to net from 12 yards before Kroos' stunning strike finally broke down the 10-man Gunners' resistance.
Szczesny was shown a straight red card by Italian referee Nicola Rizzoli after clattering Arjen Robben to concede Bayern's penalty.
"It killed the game," Wenger said.
"These rules are different in every country. In Italy they send off for these kind of fouls.
"Our keeper went genuinely for the ball. He touched Robben, who made certainly more of it. I told him (Robben).
"Wojciech misjudged the situation, there was no clear desire to make a foul, he misjudged the ball.
"The game delivered what it promised at the start. The game was until then top quality and in the second half I think it was, for neutral people, boring.
"It was one-way traffic and the referee made a decision that basically killed the game."
Szczesny made an obscene gesture when leaving the field which may invite UEFA action.
Wenger did not see the Pole's reaction and also was not aware of an incident involving Robben and Bacary Sagna.
Arsenal defender Sagna believes social media talk of the Dutchman spitting on him was false.
Sagna said: "I don't think so. Things went well with me and him tonight."
Wenger criticised former Chelsea winger Robben's reaction to Szczesny's challenge, the Frenchman suggesting the Dutchman exaggerated the contact and that Bayern were guilty of similar crimes.
"He has enough experience to know to make more of it," Wenger said. "Overall I felt that Bayern made a lot of every single contact. We are not used to that in England. We complain sometimes.
"Fouls were given today that usually are not given in the Premier League. It's different rules (in Europe) and we have to accept it."
Bayern boss Pep Guardiola refused to debate the incident and answer Wenger.
Guardiola said: "I don't answer my colleagues. I saw on TV, it's a penalty.
"(Szczesny was) the last player and the referee decided it's a penalty. The rules say (a foul by) the last man is a red card."
The incident was all the more frustrating for Arsenal as Ozil had spurned the chance to give his side the lead, his weak penalty saved by Manuel Neuer.
Without Mikel Arteta and Olivier Giroud on the field, Ozil was the nominated penalty taker, but he appeared less than confident.
Wenger added: "We needed that tonight because you could see that Bayern were on the ropes at the start of the game.
"We had three good chances in the first 15 minutes. I felt that to make them more insecure, we needed to score that penalty. But he missed it.
"He was affected by it. I think he wanted to do so well tonight that it affected him.
"You could see even five, 10 minutes later on the pitch he still was shaking his head. It had a huge impact on his performance."
Wenger's options to change the game were limited as Lukasz Fabianski had to come on in goal and Kieran Gibbs went off with a hamstring problem.
It meant Giroud was an unused substitute after being overlooked in favour of Yaya Sanogo, with Wenger insisting it had nothing to do with Giroud's alleged affair.
"Giroud is a strong character, and what happened doesn't influence his behaviour on the pitch," Wenger added.
"I just decided to give him a breather for one or two games, and to give him a chance to come back refreshed.
"Also I wanted to give an opportunity to Sanogo, and I think he did very well."
Wenger, whose side won 2-0 at Bayern last season, exiting on away goals, refused to concede defeat in the tie.
"It isn't over because we will fight until the end," he added.
Guardiola celebrated a first win at Arsenal as a manager and praised the performance of Kroos in particular.
He said: "I like players with personality. They take the ball and they want to play and play and play.
"Toni was great. An incredible goal. I'm very happy with his performance."