Leading 4-0 prior to Wednesday's return leg in the last 16, PSG suffered a humiliating defeat as they were eliminated 6-5 on aggregate following a 6-1 loss at Camp Nou.
Despite trailing 3-1 on the night after Edinson Cavani's 62nd-minute volley, PSG were still in the box seat to advance to the quarter-finals thanks to the priceless away goal, with Barca needing three goals to overhaul the French champions.
But PSG were forced to watch on helplessly as Barca scored three unanswered goals from the 88th minute - Sergi Roberto netting the 95th-minute winner - and Verratti said the Spaniards thought they were headed for the exit door before their staggering fightback.
"With Cavani's goal, we gained some peace," Verratti said via L'Equipe. "I then spoke to the players of the Barca, they told me that it was finished.
"Take three goals in seven minutes, I cannot find an explanation, it's football.
"This is a game I will never forget. I hope it will serve as a lesson to everyone."
Verratti continued: "The qualification of Barca is deserved. It was difficult to play, to make passes. They pressed too much in the first period. In the second, we got to play better.
"Now we're going to have a hard time. There will be others.
"We must find the strength to raise our heads. You have to be men. We are all sad. We lost 6-1, it's not because of the referee. We are primarily responsible."