Klopp's side emerged victorious from a goal-packed Champions League semi-final, winning 7-6 on aggregate despite losing the second leg 4-2 in Rome on Wednesday.
Liverpool were in control at 2-1 up, but Roma scored three times after the interval, although their last goal came with virtually the final kick of a record-breaking tie.
It was the highest scoring semi-final in the Champions League era and Reds boss Klopp admitted there was a little bit too much drama for his liking.
"It was just crazy. I forgot the score! It was 7-6 right? Unbelievable!" Klopp said.
"The game was wild. They took all the risks and we punished it with the counter-attack but then we gave away a goal.
"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 it's normal to have to keep nerves in.
"It was a little bit exciting, more exciting than I actually wanted."
Although Klopp would have preferred a less heart-stopping evening, he was adamant Liverpool's place in the final was just reward for their superb 5-2 first-leg win.
"We are deserved finalists 100 percent. You don't come without luck. We needed it only one time tonight. Real Madrid needed luck yesterday too. That's how it is," he said.
"The boys deserve it, the character they showed, the football they showed."
Klopp has lost five finals in his managerial career, including a 2013 Champions League loss against Bayern Munich when he was in charge of Borussia Dortmund.
After moving to Liverpool, he was beaten in the 2016 Europa League final by Sevilla, just weeks after losing the League Cup final to Manchester City.
His only cup final success as a manager was in the 2012 German Cup with Dortmund.
But the 50-year-old said beating holders Real in Kiev would be the perfect way to end his personal drought.
"We should start winning but I know that. Everyone will remind me now from now on that I have lost the last five finals but we will try and go there again," he added.
"We have two very important Premier League games, then let's go there and try our best."
Liverpool players held up a banner reading "Sean Cox -- You'll never walk alone" in tribute to the Reds fan who was left in a coma after being attacked by Roma fans at Anfield last week.
And Klopp dedicated the win to Cox, saying: "It's 100 percent a final for Sean Cox.
"We said before the game we thought about it, now we're here, all our prayers and wishes are with him."