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The win puts the Gunners in a commanding position at the top of Group F and Klopp is convinced that Arsene Wenger's side are capable of lifting the trophy, so long as they avoid Bayern on the way.
"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 sit third in Group F, three points behind second-placed Napoli, although Klopp remains convinced that his side are capable of picking up two wins in their final group matches to give themselves 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 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."