France international Mbappe took issue with the German substituting him during Saturday's 5-0 home win over Montpellier in Ligue 1, while Tuchel did not attend Neymar's 28th birthday party on Sunday.
The timing of Neymar's party became a point of discussion since the Brazilian star suffered a rib injury in Saturday's game.
The club confirmed on Monday that Neymar will sit out Tuesday's league match at Nantes with that injury, but Tuchel said his team selection wasn't influenced by the much-discussed party.
"Is it the best way to prepare for a match? No, clearly not," Tuchel told a news conference ahead of the clash with Nantes. "Is it the worst thing in the world? No."
The German coach also said it was his choice to not attend the themed fete at the Yoyo club in Paris.
"We must be clear. I decided to not attend Neymar's birthday. That was my choice. It was not against him -- it was the best thing to not be there."
Tuchel also denied there was any issue with either Neymar or Mbappe.
"There is no crisis," he said. "Personally, I am not annoyed.
"I am a coach and Kylian and Neymar are both top players. You have to handle players as part of a strong team, not a divided one.
"I am not angry with either of them. There are times when a relationship between the player and coach is easier, but that is normal."
Asked if he thought his public clash with Mbappe during the 21-year-old's substitution against Montpellier could lead to a summer exit, Tuchel rejected the idea.
"I refuse to believe Kylian will use this episode to try to leave the club this summer," the former Borussia Dortmund boss said. "He has a contract and is our player."