The Catalans became the first side to come back from a 4-0 first leg deficit as Neymar scored twice in the final two minutes.
The Catalans became the first side to come back from a 4-0 first leg deficit as Neymar scored twice in the final two minutes and then teed up a 95th-minute winner by Sergi Roberto to reach the quarter-finals 6-5 on aggregate.
"This is the best game I have ever played. For what it meant, for what we experienced and because I am in great form," the Brazilian told BeIN Sports.
Luis Suarez's early opener, a Layvin Kurzawa own goal and Lionel Messi's penalty put Barca 3-0 up inside 50 minutes.
However, the Spanish champions looked down and out when Edison Cavani volleyed home what seemed to be the clinching away goal for PSG.
"Before... we believed and now even more," Neymar added on Barca's chances winning a sixth Champions League.
"When they scored the goal we had a little dip but then there was the fourth and the penalty. We concentrated and Sergi's goal came.
"I know that we have made history. A team like this can do anything. The game was lost and we went out to play without pressure and with joy, throwing everything forward."
Barca boss Luis Enrique announced last week that he will leave the club at the end of the season after he was heavily criticised following their 4-0 humiliation in Paris three weeks ago.
And Enrique took the chance to round on his critics as he thanked the "faith" of the Barca players and fans.
"First we had the mourning and that was especially hard on one person," he said.
"This victory is dedicated to all Barca fans, but especially those that had faith in their team even after a day in which they were clearly outplayed by a team like PSG."
Defender Gerard Pique even predicted a baby boom in the Catalan capital set off by Roberto's outstretched right leg sparking delirium among nearly 100,000 at the Camp Nou.
"I would say to the hospitals of Barcelona to hire nurses. Tonight people will make a lot of love," said Pique, the partner of Colombian pop star Shakira.
"It's a miracle. We are in the quarters, which was the objective before it got a lot more complicated in Paris," said Pique.
"We never stopped believing, even the fans, who are normally the most pessimistic. It seems this new generation believes in the team more.
"We have done it all together and that helps a lot."
Despite Neymar, Suarez and Messi's heroics, it was Roberto who proved to be Barca's unlikely hero as he choose the perfect time to score his first goal of the season.
"I threw myself at it with everything," said the Spanish international.
"We left Paris very down and now this is incredible. We were prepared for all this. The fans were like 10 extra players and in the end this is all for them."
And Enrique confessed he had questioned why Roberto doesn't find the net with more regularity.
"I saw him score a lot of goals in the youth team and it is always a joke between us 'why doesn't Sergi Roberto score?' And then he scores tonight," added Enrique.
"This sport is indescribable."