The Gunners took the lead within the first three minutes at the Allianz Arena, as Olivier Giroud tapped in from close range before Laurent Koscielny levelled the aggregate score four minutes from time.
Bayern’s three goals scored at the Emirates Stadium meant they scraped through by the virtue of away goals, but Wenger praised his team’s display and was happy they showed that they at least deserved to be there.
Speaking to reporters, Wenger said: "I am very proud of the team but very disappointed for everyone who follows Arsenal that we didn't get the third goal.
"Qualifying is 180 minutes but our first 90 was not our best. I believe it was very possible to knock Bayern out. Overall, at least we have shown we deserved to be there.
"They are a very defensive team and stopped us playing tonight. Honestly, the referee tonight was a bit difficult for us. We had not the same opinion on some situations.
“I believe our defence played very well overall. They looked in control and were solid defensively. [Carl] Jenkinson, [Per] Mertesacker, Koscielny, [Kieran] Gibbs and [Lukasz] Fabianski all had good games.
"You are never going to stop a team like Bayern creating chances."
Last season’s Champions League exit came under similar circumstances as the Gunners almost overcame AC Milan’s four-goal lead from the first leg and Wenger admits that once again a poor showing in the first meeting has proved costly.
"It is a bit similar to last year against Milan," he added. “The regret is not tonight. The regret is the first leg at home.
“We were under pressure tonight. A bad performance tonight could have been terrible for the morale of the team and pressure as well."
The most notable absentee from the Arsenal starting XI was Thomas Vermaelen, with the Belgian seemingly dropped following a string of poor performances, but Wenger would not comment on whether the defender will continue to sit matches out.
He said: "I don't want to explain that. It is possible he might play at Swansea. I haven't decided yet. I might rotate."