The coach, who had to watch the game from the stands, was thrilled with his team's effort at the Emirates.
Henrikh Mkhitaryan's opener was canceled out by Olivier Giroud's equalizer 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 perfect streak in Europe this season and consigned the Gunners 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 meters before I scored my goal and finished it," Lewandowski 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-place Napoli. Nuri Sahin is already focused on a return to Bundesliga action in the club's derby clash with archrival Schalke this weekend.
"The win will give us a boost," Sahin said. "Now we try to use the victory to our advantage against Schalke."