Both sides missed penalties in an explosive first half, with Arsenal's Mesut Ozil the first to draw a blank with David Alaba following suit for Bayern after home keeper Wojciech Szczesny had been sent off for wiping out Arjen Robben in the box.
Bayern made extra man count in the second half as Toni Kroos' sublime curling effort gave them the lead and substitute Thomas Mueller headed in Philipp Lahm's cross on 88 minutes to put the German side firmly in control of the tie.
"The referee made a decision that basically killed the game," a disgruntled Wenger said of Italian official Nicola Rizzoli's dismissal of his goalkeeper.
"I think these rules are different in every country. In Italy, they are sent off for these kind of fouls," the Frenchman added.
"I think our keeper went in for the ball and he touched Robben, who certainly made more of it and I told him.
"He (Robben) has enough experience to make more of it. Bayern made a lot of every single contact, we are not used to that in England.
"We complain sometimes and I think fouls were given today that are not normally given in the Premier League."
Arsenal started brightly and their high tempo caused problems for the Champions League holders but the game swung in the German side's favour after Ozil squandered his opportunity to put the Gunners ahead and Sczcesny saw red.
"We needed that (penalty) tonight because you could see that Bayern were on the ropes at the start of the game," Wenger said.
"We had three good chances at the start of the game and I feel to insecure them more we needed to score that penalty tonight."
Bayern beat Arsenal 3-1 at the same stage of the competition last season but scraped through on away goals after losing the home leg 2-0 and coach Pep Guardiola warned his side against complacency in the return fixture on March 11.
"After the clear penalty and red card the game changed completely," Guardiola, who won the Champions League as Barcelona coach in 2009 and 2011, said.
"It is never easy, they had nine players in the box and we waited patiently," he added.
"We now have to focus on the second leg. If we can defend the result everything can happen, but if we think we have to win the second leg it will be a better challenge."
- Sports & Recreation
- Arjen Robben
- Wojciech Szczesny
- Mesut Ozil