However, Arsenal – who had thumped Norwich 4-1 on Saturday – regrouped and were level just before half-time through Olivier Giroud before substitute Santi Cazorla curled a 20-yard effort against the woodwork.

All of Arsenal’s efforts, though, were undone as Dortmund – last season’s beaten Champions League finalists – netted with just eight minutes left on the counter-attack through Lewandowski to ruin Wenger’s 64th birthday and leave the Gunners still with work to do to qualify for the knockout stages.

“If you cannot win the game, you don’t lose it. Especially in the second half when we were on top, we made things difficult for ourselves by giving them the second goal,” said Wenger.

“We put ourselves on the back foot with the first goal and (we were) naive for the second goal.

“If you look at the number of saves our keeper had to make and you concede two goals, you can say that we can only look at ourselves for not being mature enough in situations like that.”

Lewandowski, though, could well have earlier been shown a red card rather than only a yellow from Swedish referee Jonas Eriksson when he clashed with Laurent Koscielny, and seemed to catch the defender with a stray elbow.

Wenger said: “It looked like (it could have been a red card), but I haven’t seen it well, but the referee was in a much better position than I was and didn’t decide to do it.”

England midfielder Jack Wilshere was replaced in the second half having been troubled by an ankle problem, which is not expected to keep him out of the weekend’s game at Crystal Palace.

“At the moment it is his desire to play that gets him through the game,” Wenger said.

“We will see how he responds in the next two or three days, we have to wait for the medical assessment.”

Arsenal now find themselves in a three-way fight for top spot in their group on six points, along with Dortmund and Napoli – who beat Marseille 2-1 – and will need a better result when they travel to Germany in two weeks’ time.

“It is tight and difficult for us, but possible,” Wenger said.

“We need a result away from home, but we can do that.”

Dortmund boss Jurgen Klopp, who watched from the stands because of a touchline ban, felt his side were worth their victory.

“Winning abroad in London, of course you need a bit of luck for that, but if you manage to make the difference with one extra goal then I think you also deserve it,” he said.

“We didn’t come here to dominate Arsenal in London, we came here to get a result and that is what we did.”