By ESPNSTAR.com staff
Despite Mats Hummels missing a penalty three minutes before the hour mark, Robert Lewandowski's 87th-minute strike ensured BVB got their Group D campaign off to a perfect start.
Following last term's disappointment of an early elimination in the competition after Dortmund finished bottom of a group consisting of Arsenal, Marseille and Olympiacos, Klopp believes his side have shown signs of improvement.
"It was an unbelievable match," he said on UEFA's official website. "It was very intense, because our opponents have so much talent in their team.
"Whenever there was space, Ajax became dangerous. We defended well and finally scored in the end.
"I always believed we would do it, even though we had missed a couple of earlier opportunities. Robert then did a fantastic job.
"Our development has been going on for quite a while, we are constantly evolving. Today [Tuesday] there were a couple of things which we can do a lot better, but we are sticking to our principles and our plan was to be very lively."
Dortmund return to Bundesliga action on Saturday when they visit struggling Hamburg.