Dortmund found themselves trailing their hosts 2-0 at half-time thanks to goals from Jerome Boateng and Thomas Muller, with Bayern good value for that lead.
It could have been even worse for Dortmund, as Arturo Vidal hit the crossbar early on in a solid opening 45 for the hosts.
Dortmund improved after the break and Shinji Kagawa went close, before Andriy Yarmolenko headed in following a fine assist from the Japan international.
Youngster Alexander Isak had an excellent chance to equalize late go wanting after a poor first touch and Dortmund were ultimately made to pay for starting too slowly.
"I felt we were really in the game for the last twenty minutes," Stoger told reporters.
"It does not matter if I'm angry now - I'm more annoyed about how we performed in the first half. That was inactive and not as we would have liked and as we imagined.
"I think it would have been exciting if we had gone into extra time, because I felt that we were physically in a good shape.
"But if you have to be lucky for a long time that the game was not clearly decided earlier, then you do not need to mourn for a chance to score in the 92nd minute."