Arsène Wenger lamented a "massive wake-up call" for English football as Arsenal became the nation's final team to exit the Champions League on a night of drama and gallant failure at Bayern Munich.

Arsenal won 2-0 here only to come up short on the away goals rule and suffer a third consecutive elimination at the last-16 stage of the competition. The regrets were not located here, rather in the first leg at home and, in particular, the concession of the late third goal to Mario Mandzukic which proved decisive.

"It's a massive disappointment for English football because for many years we have not been used to this," Wenger said, as he reflected on Champions League quarter-finals without English representation for the first time since 1996, Arsenal following Manchester United, Chelsea and Manchester City in going out.

"It's a massive wake-up call for us and it means that the rest of European football has caught up with us. We have to take that into consideration when we talk about the Premier League in the future."

Arsenal took an early lead here through Olivier Giroud and Laurent Koscielny scored their second on 87 minutes to hint at a historic triumph. There was valour in the exit but Arsenal's irritation lay in leaving themselves with too much to do.

"To qualify is 180 minutes," said Wenger, who will definitely now go an eighth straight season without a trophy. "It's a bit similar to last year's situation against Milan, when we missed the first leg [and lost 4-0]. The regret we have is not this game against Bayern but the first game. You could see tonight the weight of that third goal that we gave away with four minutes to go. It's massive.

"We went close and I am very proud of the performance but as well I am very disappointed for everyone who follows Arsenal. When you look at our game tonight we have many regrets about the first game.

"I felt it was very feasible to knock Bayern out. We had a plan that we respected tonight. It went a bit for us on some occasions but overall we played well. The second goal came too late but we did have a few opportunities in the second half. Bayern defended very well. They were a very defensive team tonight and they stopped us from playing. We were under pressure because a bad performance would have been terrible for the morale and the pride of the team. The regret I have is that there is potential in the team and we are, of course, out of the competition."

Wenger had been expected to rotate his personnel ahead of the Swansea game but he picked Theo Walcott and Santi Cazorla, and the surprise was the omission of the captain Thomas Vermaelen. Wenger, who offered honourable mentions to each of his starting back five, was snappy about the reasons for Vermaelen's presence among the substitutes. "I don't want to explain too much," he said. "I don't know if he will play at Swansea. We have to see tomorrow or Friday. It's possible yes. I want to see how everybody recovers. We will rotate a bit at the back and in midfield. It's a massive game on Saturday."

The Bayern manager, Jupp Heynckes, admitted that his team had "got away with a black eye". He added: "These are the most difficult games and you have to finish them. We fought hard but we didn't play well, although I have to say we had great chances. We should have taken advantage of them. Arsenal came here wounded and they had a good game."