Klopp: Result does not reflect the game
Pep Guardiola's men were triumphant in the clash between the title contenders played at Signal Iduna Park, stretching their unbeaten record in the Bundesliga to 38 games.
The scoreline was somewhat harsh on a Dortmund side who had more than held their own, especially in the first half when Robert Lewandowski spurned a glorious close-range opportunity to put his side ahead.
Bayern stepped up a gear in the final 30 minutes, however, as former Dortmund star Mario Gotze opening the scoring with a deft finish with the outside of his boot, before a neat chip from Arjen Robben and Thomas Muller's effort rounded off the victory.
But Klopp believes the scoreline is immaterial, and rued his side's inability to take chances.
"I do not care how badly we lost," Klopp told Sky. "Bayern played differently. They played many long balls and they were very patient.
"We had the better chances until 1-0 and we had a huge chance to make it 1-1.
"But you have to convert these chances. After the second goal you could see the team had a crack. I don't care about the third goal."
The loss leaves Dortmund third in the Bundesliga standings, seven points adrift of table-toppers Bayern.