Ferran Torres had Barca ahead before PSG fought back through goals from youngster Senny Mayulu and Goncalo Ramos.
Flick later said of the defeat: "We played much better in the first half than in the second.
"We concede too many goals because of fatigue. PSG is a great team, they have very young and fast players, and they had a fantastic match.
"We didn't play at our best, and against an opponent like that, it's necessary. They deserved the victory.
"When you defend a 1-1 draw, you have to play more intelligently at the end of the game, and that didn't happen. They scored on us in a transition. We have to be more structured and cover all the spaces.
"We're very disappointed, and that's understandable because we wanted to show a better performance today."