Dortmund went 1-0 up via Marco Reus, but Javi Martinez and Mats Hummels then struck to hand Bayern the lead at half-time on Wednesday.
The Bavarians had a number of chances to put the match to bed, but poor finishing kept Dortmund's chances alive and Pierre-Emerick Aubameyang and Ousmane Dembele eventually fired them to the final.
"We came back and turned things around in Munich, that is just madness," Tuchel told reporters.
"We completely lost our footing after the first 20 minutes. We lost too many duels.
"We then had enormous luck after the break when [Sven] Bender prevented [Arjen] Robben from scoring Bayern's third. We would have lost the game had that gone in. We then scored two great goals and held on.
"We had the little bit of luck that's necessary when you come here. You could even say a lot of luck, but you need it here. This win is huge for the team's confidence and development."
Dembele led Dortmund the way with an assist and a goal and the Frenchman feels Wednesday's game was arguably the biggest moment of his career.
"I am very happy to have reached the final in Berlin," Dembele said.
"Bayern have a great team, so you need a bit of luck to beat them.
"This is the biggest moment of my career so far. I will not forget that assist and goal lightly."