The Gunners became the first English side to win in the Westfalenstadion after Aaron Ramsey continued his run of form with the only goal in the 62nd minute.
"We were under consistent pressure from the first to the last minute and we didn't make mistakes," Wenger told Sky Sports.
"It was a very tight game, very difficult, but we were united and had a compact block which didn't give them room to create chances.
"We knew at half-time it was a question of keeping our team focus without making a mistake and letting our technical superiority come in at some stage of the game.
"We came into the game and suddenly we looked like we could score.
"I was concerned it was a long time to go when we scored but after that we created chances and could've scored a second goal and they (Dortmund) tired a little bit as well
"We looked stable defensively. We were under pressure but we had a good mixture of technical awareness and attitude. Overall it was a very mature performance.
"If you look at the results they have made at home in the Champions League, not many teams have achieved that."
Wenger continued: "We looked more stable defensively because we have experience in midfield not to lose the ball in stupid positions.
"Dortmund are especially dangerous when you lose the ball, and to counter that, you need maturity. I have a lot of respect for Dortmund because they are a very good side.
"Unfortunately this group is a very strong group, and one of the big teams will have to pay a heavy price. I hope it will not be us."
Arsenal had come into the tie on the back of a 2-0 victory over Liverpool which moved them five points clear at the top of the Barclays Premier League table, and Wenger challenged his men to produce another composed display when they travel to Manchester United on Sunday.
"I just hope that it strengthens the belief of my team that we can put another great performance in," he said.
"You know we have another massive game on Sunday, and we want that kind of performance again."
On Ramsey he added: "A year ago I thought it would be difficult for him to score but he is a young player and is confident and has improved tremendously - which is a huge credit to him."
Ramsey hailed a classic European away display and added: "It was a great achievement from the lads. It is always a difficult place to come. We realise that from the last time we came here and drew 1-1.
"They got to the final last year and were unlucky and they are a strong team so we had to do our defensive work.
"We were very good defensively even thought we didn't have any shots in the first half and they had a few, even if it was from distance.
"We kept our shape really well, we were patient and it was a proper away performance from the lads and we got them on the counter-attack."
On his own goalscoring run after an 11th goal of the season Ramsey added: "I am enjoying myself at the moment and everything seems to be going in.
"I'm delighted with the way I'm playing and the goals I'm scoring."