Senegal international Mane was fined and will miss Saturday's Bundesliga game against Hoffenheim as part of a one-match suspension after hitting Sane following Tuesday's Champions League quarter-final first leg 3-0 loss at City.
Sane suffered a cut lip in the altercation and the two, who were also seen arguing on the pitch late in the game, had to be separated by team mates.
"I am the first one to defend Sadio. I have known him a long time and I know him as a top pro," Tuchel told a news conference. "He is football pure. He has my deepest trust after the mistake he made."
"Everyone can make a mistake. It went against the team's code of conduct. That's clear."
Mane, a two times African footballer of the year who joined Bayern last year, had complained about the way Germany winger Sane spoke to him after the defeat at the Etihad Stadium.
They both trained together on Thursday as Bayern look to find some stability after a rocky few weeks that included last week's shock German Cup exit at home to Freiburg.
The Bavarians are two points clear at the top of the Bundesliga with seven games remaining.
"It was important that it was cleared quickly," Tuchel, who took over from sacked Julian Nagelsmann (35) in late March, said.
"That had a cleansing effect. It was important that he remained in training even if he has this one-match ban. Because we had to deal with it and it was an blatant incident we had to clear it before the next training," he said.
"We did it yesterday. We cleared the air so we can train in a positive way. We are not the first and most likely not the last for it to happen to."
Bayern face City in the return leg on Wednesday.