Mauricio Pochettino's charges suffered their second defeat of the season after going down 3-1 at the Stade de la Beaujoire.
The Italian midfielder did not hold back in the assesment of the referee after the encounter after he felt Nantes should have been reduced to 10 players.
"The referee should have given [Dennis] Appiah the second yellow for the foul he made [on Mbappe]," Verratti fired to Canal+ after the final whistle.
"How is it possible not to give him the yellow? We got sh*t on by the referees!"
PSG sporting director Leonardo echoed Verratti's sentiments and felt the referee should have had more control of the game.
"The referee should have controlled better. With the fouls committed, we risk having players unavailable for 3 months like the foul on Kylian," he said to Canal+.
"There is also the fact that we announced one minute of additional time in the first half and the penalty is whistled at the 49th minute!
"I don't want to be here to cry. It's deserved to lose, but against us there is this desire to whistle against us. It's embarrassing."