PSG again failed to wrap up the Ligue 1 title after suffering a second straight loss, a Diego Carlos double lifting Nantes to an upset win.
Kylian Mbappe was dropped for the encounter and PSG lost their third league game of the season, although they are still 17 points clear at the top.
Tuchel, whose team had gone ahead through Dani Alves, said he was unable to defend his players' display.
"Today, we didn't perform in 90 minutes. There was no performance, no performance at all. So it was impossible to win.
"We can lose, we can do mistakes, and we [the club] will always defend players if they play with a good mentality, with desire and as a team.
"I always defend my players, but today it's not possible."
Diego's brace and an Abdul Majeed Waris goal gave Nantes control after Alves' opener, and PSG were beaten despite Metehan Guclu's late strike.
Tuchel slammed PSG's performance, saying they were fortunate the defeat was not even greater.
"We played very, very bad. Nantes deserved to win. We should happy we didn't lose 4-1 or 5-1. It is easy to analyse," he said.
"I don't know what we lacked, but it is the reality. It was a very, very bad game. We deserved to lose."
The right results in either match would see the club claim the crown with just six matches remaining in the season.