The former Barca great suffered the first defeat of his managerial reign as goals from David Luiz, Marco Verratti and Blaise Matuidi helped wrap up the points for the hosts.
Lionel Messi and Neymar were on target for Barca, who introduced Xavi off the bench for a record 143rd UEFA Champions League appearance.
However, PSG deservedly picked up their first European win of the campaign and Luis Enrique paid tribute to the French champions.
"I am not surprised by PSG. They have the potential to win the Champions League," he said.
"They're a squad that consists of a lot of top-level players, internationals, and we knew they would be very competitive.
"This is a game in which errors are costly, and we made some; the first defeat had to come someday."
Barca now sit second in Group F, although they could have salvaged a point following a flurry of late chances, with Munir El Haddadi hitting Salvatore Sirigu's left-hand post.
Luis Enrique was pleased with the impact his substitutes made, explaining: "Munir El Haddadi had an effort, Xavi gave us more vision and Sandro [Ramirez] was also very good.
"I think the changes were the correct ones. We sit second but we knew it wasn't going to be easy, it is the Champions League group stage and it is never easy."
