All of Arsenal's efforts, though, were undone as Dortmund - last season's beaten 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.
"We put ourselves on the back foot with the first goal and naive for the second goal," he said. "If you look at the number of saves our keeper had to make tonight and you concede two goals, you can say that we can only look at ourselves for not being mature enough in situations like that.
"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."
Lewandowski's goal came after a lucky escape for the Pole, who was only shown a yellow card by Swedish referee Jonas Eriksson when he clashed with Laurent Koscielny, and looked to have caught the defender with a stray elbow.
"It looked like [it could have been a red card] but I haven't seen it well," Wenger added. "But the referee was in a much better position than I was and didn't decide to do it. I will have to look at it again, I don't know."
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.
Wenger said: "You could see that he was not completely himself and that is why I decided to take him off.
"At the moment it is his desire to play that gets him through the game. It looks like he was handicapped after the first tackle he got. He looked like he landed awkwardly. He looked to me that he limped a little bit.
"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," said Wenger. "You have three teams with six points, and we have played twice at home and once away, so that means 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 the worthy victors in London.
"I saw my team fighting and for us we deserved to win this game," he said.
"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.
"If you watched this game not for Arsenal and not for Dortmund, you can say maybe Arsenal had some better situations but they played at home and we didn't come here to dominate Arsenal in London, we came here to get a result and that's what we did."
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