The Gunners were 2-0 victors on the night thanks to an early Olivier Giroud strike and a late Laurent Koscielny goal, but after their 3-1 defeat in north London it was the German side who progressed on away goals.
Mario Mandzukic's late third goal was the difference between the two sides over the two legs and it is a goal which still irks Wenger.
"When you lose at home, you make it difficult for yourself," he said.
"We played against one of the best teams in Europe. The spirit and the performance was there we had a great go.
"My regret from first game is that we conceded a cheap goal in the last five minutes when we could lose 2-1 at home. You can see how important that goal was tonight."
Despite his frustrations, a victory against a side 20 points clear in the Bundesliga did give some comfort to the Frenchman.
"I am confident we will give everything to come back next season. Our young players done very well lets finish well this season strongly."
Meanwhile, debutants Malaga kept their Champions League dream alive when Isco and substitute Roque Santa Cruz struck in a 2-0 win at home to 10-man Porto that sent the La Liga side through to the last eight 2-1 on aggregate.