Asked if he ever seen a game like that before, Klopp told Sky Sports: "No, I wouldn't have. I did wish today I would see this.
"This is one face of football - one very disappointed team in this moment and one lucky team - it was unbelievable.
"We made, I think, our worst game in the Champions League. The first half we showed a bit of nerves - not our best football.
"In the second half we tried a bit better and they were two clever this evening, it was not easy.
"We got the goal and we made it. It is unbelievable what happens in this stadium - it was crazy."
Klopp continued: "I think I have to go to the doctor, but it was really crazy it was a like a championship, it's not a championship, but it felt like it.
"In the dressing room my assistants and me were looking at each other in shock. We are in the semi-final, nobody could believe who knew us a few years ago. Now it's really crazy but one of the best things I have ever felt."
Asked if his side could go on to win the Champions League, Klopp added: "If we play like tonight, no, but if we play like we have in the Champions League, the passion of tonight we are really hard to play, difficult to play as we will see but now we have got the target and we reached it."