Klopp, who is reportedly set to be offered a contract extension at Anfield, was emotional seeing the support for the Reds after their latest success in Europe.
"I cannot really describe it because I cried a little bit as well because it's so overwhelming what the people are doing," he said, via the club's website.
"When you have a direct eye contact and you see how much it means to them that's touching to be honest. It's brilliant.
"Thank God the weather changed in a positive direction so we are having a wonderful time here. It's really special."
Klopp, who claimed his first trophy since taking charge at Anfield in October 2015, said the parade was an amazing experience for himself in seeing how much of an impact his club had on the city.
"I don't know exactly how many people live in Liverpool but there's not a lot of space for fans and supporters of other clubs, so it's incredible," he said.
"This team is really doing so well and if you are a young kid which team would you support? There are not a lot of other options and opportunities apart from Liverpool so it's really nice to see.
"You see in their eyes how much it means. It's unbelievable and it's so intense. Today, wow! It's crazy."
Club's owner John Henry was also there, alongside chairman Tom Werner, to take in the celebration of their first Champions League success since Fenway Sports Group took over the club nine years ago.
Liverpool completed the success just a year after last reaching the final, when they lost 3-1 to Real Madrid.