Liverpool lost 4-2 in Rome on Wednesday night but went through 7-6 on aggregate.
They had been 5-0 up at Anfield at one point in the first leg - but endured worrying instability in defence to let Roma back into the tie.
Real themselves were pushed to the limit by Bayern Munich but eventually prevailed over the double-header.
The two sides meet in the final in Kiev on March 26 and Klopp is adamant his Reds side deserved to be there.
"We are deserved finalists 100 per cent,” he said.
You don’t come without luck. We needed it only one time tonight. Real Madrid needed luck yesterday too. That’s how it is.
“We have two very important Premier League games then let's go there [the final] and try our best.
“The boys deserve it, the character they showed, the football they showed - it was just crazy. I forgot the score! It was 7-6 right? Unbelievable!"
Liverpool still have Premier League fixtures against Chelsea and Brighton to play before they turn their heads back to the Champions League.
This will be the third final they have reached in Klopp’s tenure - but they are yet to win a trophy.
Discussing his final record with the Anfield club, the German boss said: “We should start winning but I know that.
“Everyone will remind me now from now on that I have lost the last five finals (also with Borussia Dortmund) but we will try and go there again."
Liverpool twice went ahead in the Stadio Olimpico thanks to Sadio Mane and Gini Wijnaldum goals, only for Roma to hit back and then make a game of it with two very late strikes.
Discussing the erratic match, Klopp added: “The game was wild. They took all the risks and we punished it with the counter-attack but then we gave away a goal.
“There was lots of space. But then our last line was too deep and you cannot play like this. Each counter-attack was really dangerous for us but we didn’t use this. We were a little too patient. We are usually much better - you know this.
“It was the first semi-final for most of the boys so normal to have to keep nerves in. It was a little bit exciting – more exciting than I actually wanted."