Tuchel, who will leave Bayern at the end of the season after just over a year in charge, said he kicked a box in the changing room during his speech to his players with the German champions desperate for a win to turn their season around.
The Bavarians had won just one of their previous five matches in all competitions before Tuesday's game.
"The motivational speech before the game cost me my right toe," Tuchel said. "I was treated on the spot but did not have the courage to take the shoe off because I did not think I would get it back on."
Tuchel spent the game on the bench sitting down as his team won 3-1 on aggregate thanks to two goals from Bayern top scorer Harry Kane and veteran Thomas Mueller.
"They (players) must have wondered why I was sitting down for the entire 90 minutes," he said.
Bayern, who won the previous 11 consecutive league titles, are 10 points behind leaders Bayer Leverkusen in the Bundesliga and are also out of the German Cup.
