The coach, who had to watch the game from the stands, was thrilled with his team's efforts at the Emirates and Robert Lewandowski branded the win important
Henrikh Mkhitaryan's opener was cancelled out by Olivier Giroud's equaliser before Robert Lewandowski sealed the three points for BVB with a late winner.
And Klopp, who was forced to watch from the stands due to a suspension, was thrilled that the Gunners were largely kept at bay.
"It was a great performance," Klopp told Sky. "We won away at Arsenal who are in a sensational form.
"It was an open game we won thanks to a fantastic attack which made it 2-1. Arsenal are too strong to keep them away from our goal the whole time. They didn't have that many chances.
"From up in the stands you have a better view! A totally new perspective."
Lewandowski's goal ended Arsenal's 100 per cent streak in Europe this season and consigned them to their first defeat since the opening day of the season against Aston Villa, which the Pole believes could be crucial in qualifying from a tough Group F.
"I ran many metres before I scored my goal and finished it," he said. "It is an important goal and an important win."
The away victory leaves Dortmund top of Group F on goal difference, level on points with Arsene Wenger's men and third-placed Napoli, though Nuri Sahin is already focused on a return to Bundesliga action in their derby clash with arch-rivals Schalke this weekend.
"The win will give us a boost," the loanee from Real Madrid said. "Now we try to use the victory to our advantage against Schalke."