PSG, still seeking a first Champions League crown after a series of knockout disappointments, were without strike trio Neymar, Edinson Cavani and Kylian Mbappe for Wednesday's Group A game in Paris.
But PSG still easily beat a struggling Madrid side thanks to a double from Angel Di Maria and a late strike from Thomas Meunier midweek.
A delighted Tuchel warned PSG's absent stars they will have to learn from the performances of Di Maria, Mauro Icardi and Pablo Sarabia, who started as the front three.
"I'm very happy with the whole team because it was really difficult," Tuchel said to RMC Sport.
"We had a lot of chances, but there were also some stages for Real where we suffered.
"But we stayed structured, always tight, aggressive and compact. Really, it was a complete performance.
"Mbappe and Neymar saw the match, and they have to do what the others did on their return.
"A problem for the coach? That's good, but we are happy to have such a team, which was not always the case.
"We can make a good team match without our stars, and it's absolutely necessary.
"I should make tough decisions, but it's good, the competition must be like that in a club like PSG."
Idrissa Gueye thrived in midfield on his first Champions League appearance for PSG since signing from Everton.
The Senegal international added balance to PSG's side, bite in the middle of the park and helped create Di Maria's second strike.
"It's good that he's with us," Tuchel added. "He is very important to us, he has a lot of qualities and he is very humble.
"He is huge. He was there with Marquinhos in the middle, and it was a good partnership. We are happy with their match."