I can't wait for Champions League semi-final - Klopp
It is the third time in five seasons Klopp has led Liverpool to the last four of Europe's elite competition.
Liverpool are in contention to win the quadruple this season having already lifted the League Cup, while reaching the final of the FA Cup.
"Each game should feel like a final," said Klopp.
"It is absolutely special to be a part of the semi-final, it's crazy. It's a massive game. So many coaches and players work their socks off their whole life and don't get a chance to be close to a semi-final.
"We are there so we have to cherish it and enjoy it as well."
Liverpool captain Jordan Henderson said what the team have achieved under Klopp so far is "very special" but there is "still a long way to go" as they bid to win the quadruple.
"I know how quickly football can change. People talk about the things we can win but we know [if we have] a couple of bad games it can all be over," he said.
"It's about keeping focus on the next game, the next challenge - whatever the competition - and see where we are at the end of the season."
Liverpool could face Manchester City - who they trail by a point in the Premier League title race - in the final should both teams progress from their respective semi-finals.
But Klopp said Liverpool will not underestimate Spain's Villarreal, who knocked out Bayern Munich in the quarter-finals and Juventus in the last 16.
"We face a very difficult opponent. They are made for the competition, the way they set-up is really good," the German added.
"There might have been a little advantage in their last two games where Juventus or maybe Bayern Munich might have underestimated them - but that will never happen to us, especially after these four games, there's no chance anymore.
"They are a really good football team who obviously want to be a part of the final but it's the same importance for us."
Jurgen Klopp guided Liverpool to the Europa League final in his first season but suffered defeat to Unai Emery's Sevilla
Klopp lost to Villarreal manager Unai Emery, who was in charge of Sevilla at the time, in the 2015-16 Europa League final during his first season at Liverpool.
But Liverpool reached the first of back-to-back Champions League finals two years later and won the competition in 2019.
Klopp said the Europa League loss was "tough" to take but was important in Liverpool's journey to success.
"I haven't thought about that for a while. It was important. I said that night, I thought we'd come back from that moment stronger and we did," he said.
"That night was a tough one to take. It was game number 64 of that season, a tough season. We can not really compare football games."
Henderson was on the bench as Sevilla came from behind to beat Liverpool 3-1 in Basel.
"That night always sticks out for me because after the game, going back to the hotel, all the lads were disappointed and you just wanted to go back to your room and get your head down," he said.
"The gaffer was a bit different to what you'd expect. He had everyone down in the bar area. I felt he knew that this was the start of something special to come.
"It was very difficult to think that then, having just lost a final, but I always felt he knew what was coming in the next few years. He has proven that was the beginning of something special."
-- Courtesy of BBC Sport