"We have won five times and that shows that we still want to keep winning," said Tuchel.
However, there is little doubt that PSG will face a much more difficult test at Anfield at the opening of their Champions League group than they did here against Saint-Etienne.
"I am also pleased that we have played without having our head turned by the game on Tuesday," added the German PSG coach.
"I have ideas (about their lineup) but I'm still reflecting on them, I'll talk to the key players and I'll be watching Liverpool's game against Tottenham and I'll decide on Monday."
Mbappe was absent when he started a three-game ban following his red card in the victory in Nimes just before the international break, and Neymar sat next to him in the crowd, rested after playing for Brazil in a friendly in the United States in weekday.
Being without the two most expensive players in the world was not a problem for the reigning champions, with Tuchel able to give Draxler his first start of the season, while midfielder Marco Verratti appeared in a Ligue 1 game for the first time since March.
There was also a debut for Spanish left back Juan Bernat after his recent switch from Bayern Munich, and although the visitors started well enough, PSG never looked back after taking the lead midway through the first half.
Verratti's ball over the top found Draxler in the box, with the German midfielder controlling the ball with his head and then nodding his head towards Saint-Etienne goalkeeper Stephane Ruffier.
The Saint-Etienne players wore T-shirts with the name of William Gomis, a former youth player of the club who was shot dead in the south of France earlier this week.
PSG's second goal came just after the break, with Cavani converting a penalty, his third goal in the same amount of games this season, after Loic Perrin had cut him in the box.
With PSG goalkeeper Alphonse Areola, favorite of Gianluigi Buffon and fresh from winning his first two senior matches for France, a virtual spectator, the hosts added two goals later.
Diaby, the 19-year-old girl who was sent at the start of the second half in place of Lassana Diarra, helped Di Maria shoot a shot to the roof of the net for the third.
Then, Diaby rounded up the score after Cavani hit a reduction of Draxler had become a help for the teenager.
Earlier on Friday, Nice shook the absence of Mario Balotelli when they came from behind to beat Rennes 2-1 on the French Riviera.
An own goal from Malang Sarr allowed Rennes to take the lead, but Allan Saint-Maximin equalized before Pierre Lees-Melou's goal in the 89th minute for Patrick Vieira's team.
Lyon prepares for his Champions League trip to Manchester City next week by going to Caen on Saturday night.
The other contenders of the Champions League in France are Monaco, who will face Toulouse in form on Saturday night before hosting Atlético de Madrid on Tuesday.