The Gunners had hauled themselves back into an eagerly-anticipated UEFA Champions League clash, with the scores locked at 1-1 as they pushed for a winner.
They were, however, to leave themselves open at the back and Dortmund swept forward eight minutes from time, allowing Kevin Grosskreutz to provide the delivery for Robert Lewandowski to volley home a dramatic clincher.
Wenger admitted afterwards that his side had become too adventurous and were left to pay the price.
He told Sky Sports: "It's difficult to take because I would agree that we were maybe not at our most fluent tonight going forward, but at that moment we were on top.
"We lost the game because we maybe wanted so much to win it that we forgot that if you cannot win it, don't lose it. That's what is most annoying because we put a lot of effort in.
"We started hesitant. At the end of the day, we went 1-0 down and when you don't start well it is difficult to get back into the game. But we did well and in the second half we were on top of it.
"We just forgot to be cautious. We were not cautious enough and we paid for it."
With Napoli seeing off Marseille 2-1 in Tuesday's other Group F fixture, there are now three sides sat on six points after three outings.
Asked what it will take for the Gunners to remain on course for the knockout stage, ahead of a return date in Dortmund on 6th November, Wenger added: "It will take three points away from home now."