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 leveled the aggregate score four minutes from time.
Bayern’s three goals scored at the Emirates Stadium meant it scraped through by the virtue of away goals, but Wenger praised his men’s display and was happy they showed that they at least deserved to be there.
"I am very proud of the team but very disappointed for everyone who follows Arsenal that we didn't get the third goal," Wenger told reporters.
"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."
Last season’s Champions League exit came under similar circumstances as the Gunners almost eradicated 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."