Mario Mandzukic put the Bavarians in front on the hour mark before Ilkay Gundogan leveled the score minutes later from the penalty spot, only for Arjen Robben to strike the winner with a minute of normal time remaining.
Dortmund enjoyed the better of the opening period and Bayern had goalkeeper Manuel Neuer to thank on more than one occasion as he kept BVB at bay.
But ultimately the firepower of the Bundesliga champion proved key, and Kehl - who was an unused substitute on the night - was quick to acknowledge that key difference between the sides.
"I believe that we have made a fantastic game. It was critical that we scored in the first half, after the start we made. But we are proud of what we have done," Kehl said.
After the game Dortmund boss Jurgen Klopp vowed that his side would be back, but that will be easier said than done with Mario Gotze set to join Bayern in the summer and Robert Lewandowski rumored to be following him to the Allianz Arena.
FCB coach Jupp Heynckes then stated his belief that the Poland striker "would not hang around," as the battle between the two Bundesliga sides continues off the pitch in the transfer market.