Few expected to see the Reds make it to next month's Madrid final after a 3-0 first-leg defeat at the Nou Camp, but the five-time European champions will now face Ajax or Tottenham after digging deep in stunning fashion.
Liverpool went ahead after just seven minutes through Divock Origi and kicked on in the second half, when substitute
Georginio Wijnaldum's quick-fire brace was followed by Origi notching from a quick corner to seal a 4-0 win and progress 4-3 on aggregate.
It capped a remarkable night, arguably one of the best in the club's history, and when asked where this victory ranks in his own career, manager Klopp said with a smile: "Top three. It's a special night, very special. Winning against Barcelona is obviously one of the most difficult things in the world of football.
"Winning against Barcelona when you're 3-0 down, makes it not easier. We had to score four goals and was not allowed to concede pretty much.
"We made it more difficult, so we didn't really think about it to be 100 per cent honest. We tried to build on the performance in Barcelona and all the good things we did there and try to win the game step by step.
"We attacked with whatever we have and can throw on the pitch. That made it a really special game, it made us really difficult to play against tonight.
"What the boys did and that was this mix of again a big heart and football skills. It's unbelievable.
"I am really proud to be manager of this team. It's unbelievable what they did tonight. it's so special. I will remember it forever 100 per cent because I don't know if it happened before or it can happen again. I really don't know. The boys did it, so it was brilliant."