The Gunners managed just four attempts at goal, compared to the hosts' 15, and scored from their first with Aaron Ramsey heading home on 62 minutes.
Defeat for last season's runners-up leaves them in danger of missing out on the knockout stages of this year's competition. Die Schwarzgelben trail second-placed Napoli by three points, but still have to host the Serie A side.
Speaking exclusively to FourFourTwo, former Borussia Monchengladbach star credited Arsenal for the 'intelligent' way they closed out the game.
"It was very much like the first [game, a 2-1 win for Dortmund at Emirates Stadium]," he said. "There were very few clear-cut chances between two teams at a very similar level. You could tell both teams have a lot of respect for each other and were anxious not to get exposed by the opposition's quality.
"Both teams gave the ball away at times but Arsenal hit us with a lucky punch and closed out the game very intelligently.
Both teams gave the ball away but Arsenal hit us with a lucky punch
"I felt we came out of the first half well and then really applied pressure at the start of the second half. Unfortunately, that's exactly when Arsenal grabbed their goal, dropped deep and really closed down the space for us to attack. That made it relatively hard to turn things round."
The 24-year-old swapped shirts with his "idol" Tomas Rosicky, who played for Dortmund from 2001-06, after the game. The Germany international insisted his Dortmund team-mates would not be dwelling on the defeat, with crucial clashes against Napoli and Bayern Munich on the horizon.
"It wasn't a bad performance - just two top teams coming together with a lot of respect and neither of them wanting to lose this game. Unfortunately we lost but I'm sure the coach will put us back in a positive frame of mind.
"We'll be over it in a few days and can get on with the next important matches."
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