The home side pressed and frustrated Bayern for 75 minutes and held a 1-0 lead, but two goals in the final 15 saw the champions claim all three points from the contest.
"I'm lost for words," he told Bundesliga.com. "I can't really believe it. We played a very good game - finally a great team performance for over 89 minutes. We shouldn't be conceding a goal like that.
"It felt like we had won, and then in the end we've got nothing. We've denied ourselves our just reward. We've had so much bad luck so far, but if we carry on playing like we did today, we'll get lucky eventually."
The defeat kept Stuttgart in 12th in the Bundesliga.