The Bundesliga outfit displayed impressive intensity throughout and goals either side of half-time from strike duo Ciro Immobile and Pierre-Emerick Aubameyang were the least their efforts deserved.
Arsenal brought positives from Saturday's thrilling 2-2 Premier League draw against Manchester City into the Group D clash, but must now reflect on opening their Champions League campaign with a defeat for the first time in 11 years.
"I think that we were not at the requested level tonight and Dortmund deserved their win," Wenger told Sky Sports.
"To concede a goal just before and just after half-time; after that the game was difficult of course.
"Energy-wise they were at a higher level. Why exactly? I think they had a much easier game on Saturday than we had but it is not always scientifically predictable.
"But, despite our very average performance we had plenty of chances - that's a little bit the paradox of the night. We could have been leading the game but they, as well had plenty of chances."
Deadline-day signing Danny Welbeck was culpable of spurning chances immediately before both Dortmund goals, but Wenger praised the England international's overall contribution.
He said: "He was dangerous. He tired in the second half.
"He couldn't finish tonight but he looked lively. For all the rest [of the game] he did well.
"He needs a goal to get that off his shoulders."
Arsenal took a win and a draw from their two previous visits to Signal Iduna Park over the past three seasons but midfielder Mikel Arteta bemoaned the individual and collective errors that left them with an uphil task on this occasions.
"They are a top side and it is one of the most difficult stadiums in Europe - we knew that from the start," Arteta told Sky Sports.
"It was very sloppy from us to concede the goal with 20 seconds to go in the first half from our own throw-in on the other side of the pitch.
"After you are 1-0 down here it's very difficult. You have to [take] risks, they are very good on the break and we didn't perform well enough tonight.
"They've got a lot of pace and a lot of pressure up front. We couldn't cope with. We gave the ball away too many times in difficult positions.
"I think they took the game where they wanted to take it and it was a disappointing game from us."
