The Reds started off with a qualifier in August against Hoffenheim and after seeing off Manchester City in the quarter-finals and then Roma, including a nervy second leg defeat in the Stadio Olimpico, they have a meeting with defending champions Real Madrid on May 26.
"In our case, we've played in the Champions League without pressure most of the time," Klopp told uefa.com. "We entered the competition for the first time in a while and we quickly realised that we had a good chance.
"We aren't anyone else. We are Liverpool, on the way to becoming a really good team, and performing at such a high level is very cool.
"To summarise, it's been a crazy ride. But, after all, we've earned our place here."
Liverpool are the top scorers in the competition with 40, not including their six goals against Hoffenheim.
They also have three of the top four scorers in Mohamed Salah and Roberto Firmino (both 10) and Sadio Mane (nine) - Real's Cristiano Ronaldo leads the way with 15 - and have James Milner top of the assists chart with nine just ahead of Firmino.
That is reflective of the football they have played this season and is a key factor of Klopp's style of play.
"Football should be more oriented to finishing every attack with a shot on target. And that's what we do whenever possible," he added. "We didn't put a special value on that. It's just part of the game."