With a little over ten minutes remaining, Origi netted the decisive fourth goal by capitalising on an impromptu corner routine with Trent Alexander-Arnold.
Anfield erupted at the full-time whistle as Liverpool secured their place in the final for the second year running, with Klopp hailing his incredible side for their achievement.
“Against maybe the best team in the world,” Klopp said. “We weren't allowed concede. We had to score and winning with a clean sheet.
“I don't know how the boys did it. It was incredible how we defended.
“It's ten past ten, most of the children are probably in bed. These boys are fucking talented giants. It's unbelievable. It is unbelievable.
“Fine me, fine me if you want. I'm not native, I don't have better words for it. It is unbelievable.”
Klopp's made no secret of how happy he was with his side after the game, saying: “I will remember this night forever. I am really, really proud to be the manager of this team.”
He continued: “The mix of potential and unbelievable heart is a mix I've never seen before.
“In a game like this you need to be confident. To put a performance like this on the pitch is so important.
“It shows what's possible in football. It's really nice. It's unbelievable.”
First, the Reds will find out who their opponents will be in Madrid on 1 June as Ajax take a 1-0 lead back to Amsterdam for the second-leg of their semi-final tie against Tottenham on Wednesday night.