Bayern were 1-0 up and had one foot in the final when Tuchel replaced Kane with back-up striker Eric Maxim Choupo-Moting.
German-born Madrid striker Joselu levelled the match just four minutes later and scored again in the second minute of injury time as the home side took the lead on the night, winning 2-1 and 4-3 on aggregate.
Jamal Musiala was also taken off with Tuchel bringing on Bayern veteran Thomas Mueller.
Kane's substitution appeared to change the momentum of the match with Bayern in control but Tuchel told broadcaster DAZN the striker was unable to continue.
"He couldn't keep going. He played with back pain and he couldn't keep going, his back froze up," said Tuchel.
The loss means Kane's long wait for a trophy continues, with the England striker still yet to lift silverware in his club career.
