Goals from Franck Ribery and Robert Lewandowski saw Bayern go two goals up within 10 minutes, but Raphael Guerreiro pulled one back to boost BVB's hopes of salvaging a positive result.
Arjen Robben restored Bayern's two-goal lead after the break, before Lewandowski netted his second of the game against his former club to seal the win for the Bavarians.
"Overall, we did not have a chance of causing Bayern any problems at this level," Tuchel told reporters.
"We started well, but were nonetheless trailing by two goals after 10 minutes. That made things very hard for us. It was nearly impossible to turn things around.
"We kept on playing well and pulled one back, but the third goal effectively decided the game. It is a very bitter defeat.
"It was already a difficult game to begin with and the way things panned out only further complicated matters. We deservedly lost by this margin. We needed to be on top of our game in order to stand a chance."