The German was happy with the result despite the performance while dismissing controversy regarding Robert Lewandowski and Mario Gotze
Midfielder Nuri Sahin put on a masterful performance with a 30-yard goal in the first half before setting up Jakub Blaszczykowski's decisive second with an exquisite pass.
Adam Bozdek's late strike set up a nervy ending for the former German champions, but Klopp was still pleased with what he labelled a "lucky" result.
"I am very satisfied with the win," the 45-year-old revealed to reporters after the match.
"From the 10th minute we played a good game with Nuri scoring a world-class goal, though in the second we allowed the opponent too much and they came out and did well.
"But from my point of view it was not serious as it is normal that we can lose a little bit of the concentration. We are certainly not undeserved winners, just that due to their late goal it was a little lucky."
Klopp made 10 changes to the side that defeated Real Madrid 4-1 in midweek, but the trainer played down the significance of dropping stars Robert Lewandowski and Mario Gotze to the bench.
"We must not exaggerate. We talked about the record of Lewandowski [scoring in 12 consecutive matches] before. I told him that he can feel safe about his record because in the next 100 years no one will beat it," he added.
"Gotze had some muscular problems. [Ilkay] Gundogan had problems with his neck, while [Lukasz] Piszczek with his adductors. All three of them were not able to play today."
Gotze has already been confirmed as a Bayern Munich player next season after the Bavarians activated a €37 million clause in his contract.
Lewandowski is also expected to follow his team-mate out of Signal Iduna Park although Klopp has denied this.