Unai Emery's side pinned Barcelona into their own half with relentless pressure from kick-off in the last-16 tie and they did not look back from Angel Di Maria opening the scoring with an 18th-minute free-kick.
Julian Draxler made it two before the interval and, after Di Maria capped a masterful showing with a sumptuous second, PSG's top scorer Edinson Cavani completed the rout.
Barcelona midfielder Sergio Busquets told reporters afterwards that his team-mates had been found wanting tactically and, speaking at a post-match news conference, Luis Enrique did not disagree.
"It's simple, the opponent has been superior with the ball and without the ball," he said. "They have won the duels, they have been more effective and the result clearly reflects what happened on the pitch. I do not think I have to explain much.
"Let's not waste time with easy topics - it is an exciting sport and there are always complications. The responsibility is mine. If you have to individualise it, it is with the coach. The players are the same ones who have won on other days.
"At the break, 2-0 was very bad. We tried to change to get into the tie but then came the third and fourth goals."
Former Sevilla boss Emery tasted victory for only the second time in 24 attempts against Barcelona in a manner that could scarcely be more emphatic, such was PSG's dominance.
Luis Enrique identified Emery's knowledge of Barca's style as a threat before the match and he conceded afterwards his opposite number did not produce any surprises – his players just executed their game plan in a manner that overran the LaLiga champions.
"We have not been surprised at all," he said. "We talked about their pressure before the game but that does not mean we can beat it. We lost a lot of duels.
"PSG have done what we expected and been at their best. But I do not lose hope, we have to score five goals."
In reality, Barcelona need more than just hope. No team has ever recovered from such a deficit to progress in Champions League history.
"It is not the moment to talk about individual things," Luis Enrique added. "I have full confidence in my players, it's time to talk about coaches. I assume responsibility, as always.
"I repeat, we are a team that has demonstrated the ability to make great matches and results and, when we assess what has happened, we will see some options."