French World Cup winner Mbappe was sent off for pushing Teji Savanier as Ligue 1 champions PSG defeated promoted Nimes 4-2 on Saturday.
The 19-year-old put PSG ahead with their third goal before he was given his marching orders in the dying seconds for reacting to a rash Savanier challenge.
"It was a horrible foul. He had an emotional reaction," PSG head coach Tuchel said. "He was lucky not to be seriously injured.
"I want him to stay calm but in a match like that, in an atmosphere like that, it's not easy. He didn't hit somebody, he just pushed.
"I'm sad but I'm not mad."
Neymar, Angel Di Maria and Edinson Cavani were also on target as PSG made it four wins from four games to be three points clear atop the table.