Kylian Mbappe's hat-trick against his former side sealed a sixth Ligue 1 trophy in seven seasons for PSG, whose campaign was derailed by a shock Champions League last-16 defeat to Manchester United in March.
PSG head coach Tuchel celebrated the title in his maiden season at the helm, while referencing Juve's wait for European glory, which dates back to 1996.
"We had a very serious first half, we are not in our best period, but we had a good game," Tuchel said via Canal+.
"Played with a good rhythm until the hour of the game. After the third goal, we lost the ball a little more. But we won, it was important. It was always complicated.
"If we win the Coupe de France, the season will be successful, the championship shows that we have worked hard.
"The Champions League is a goal, but even Juventus have been waiting for eight years. But the goal is to win the double each year, and it is achieved."
CHAMPIONS! ALLEZ PARIS! pic.twitter.com/Ro4vmMzL40— Edi Cavani Official (@ECavaniOfficial) April 21, 2019
Neymar returned from a foot injury at home to Monaco, while PSG team-mate Edinson Cavani also made his comeback in the French capital.
Cavani came on in the second half and the Uruguay international – who has been linked with a move away from PSG – insisted he is happy to see out the remaining year of his contract.
"I am under contract here for another year," the 32-year-old forward. "I am good here, calm, and very happy with the team, as well as the supporters. That said, you never know in football."