Goals from Luis Suarez, Lionel Messi, two from Neymar, an own-goal and Sergi Roberto's last-gasp winner saw Barca through as they completed the biggest-ever comeback in Champions League history.
"I was brought to my knees. I would like to thank everyone who kept their faith after we lost 4-0. This is dedicated to them because this isn't the Harlem Globetrotters, this is football," Enrique said.
"I don't think anyone stopped believing. After seeing them sit back despite the goal, the team were incredible," he added.
"We risked everything and it paid off. You get finales like this very occasionally in football and this time it was our turn," said the cpach, who will leave Barca at the end of the season.
"A feat like this does everyone good and I'm delighted to enjoy a moment like this. The key was our efficiency. The sixth goal was scored with the hope of the fan who was on the other side of the world," he added.
Enrique’s opposite number, PSG coach Unai Emery, was understandably disappointed, but said that the French side needed to learn from the dramatic defeat.
"When we analyse it, it is true that we have missed a major opportunity," said Emery.
"The first half was our fault and we didn't manage to press or do things with the ball. We defended very deep and they had more chances to score. We made mistakes for the two first-half goals.
"We were calmer in the second half and better positioned. We improved and had a chance for 3-2. The refereeing decisions went against us and we lost everything in the closing minutes. Barcelona are capable of doing that. It was all or nothing for them in the final minutes."
"It is a negative experience for me and for the club. We need to learn from it," he said.