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The win puts the Gunners in a commanding position at the top of Group F and Klopp was impressed with Arsene Wenger's side.
"They could win it - as long as they don't play Bayern Munich," the Dortmund boss told reporters. "They are young, healthy and good technicians. They won a clever game tonight."
Dortmund currently sits third in Group F, three points behind second-placed Napoli, although Klopp remains convinced that his side is capable of picking up two wins in its final group matches to give itself a fighting chance of qualification for the last 16.
"It is a very strong group and the positive news tonight is that two wins and we will qualify," he continued.
"We created much more today up front and but they scored with their first chance of the match and we could not come back. This defeat could have been avoided. It's definitely going to get exciting from now on."