Goals from Julian Draxler and Edinson Cavani were punctuated by a pair of efforts from Angel Di Maria, sending the Parc des Princes faithful into raptures.
Barca must now complete an unprecedented turnaround to triumph in the last-16 tie, and the Brazil international confessed success is unlikely.
"It was an unusual game that hardly ever happens to us, but Paris deserve credit. They had a great game, they finished well and got to our goal well," Neymar told reporters after the match.
"Now we have to think about the next game, to see what we can do to try to turn it around, which is very difficult – practically impossible. But we cannot give up.
"It's very difficult to prepare for such a game. I do not think I've ever been in this situation.
"What I'm going to do is give my all in the next game so we can turn it around."