Supporters turned Liverpool into a sea of red as the open-top bus carrying coach Jurgen Klopp and his victorious players edged through the city.
"You see in their eyes how much it means. It's unbelievable and it's so intense. Today, wow! It's crazy," Klopp told LFC TV.
"I cannot really describe it because I cried a little bit as well because it's so overwhelming what the people are doing.
"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."
"I'm ecstatic and hungover at the same time -- the best type of hangover," said Peter Broad, 37, a social housing worker and Liverpool native who was lining the route.
Liverpool became champions of Europe for a sixth time when Mohamed Salah's second-minute penalty and Divock Origi's late strike secured a 2-0 win in the sweltering Metropolitano Stadium in Madrid.
It was a first trophy of any sort in seven years for the club and banished the memories of last year's bitter defeat to Real Madrid in the final in Kiev.
The win also represented a personal triumph for Klopp, who finally snapped his run of six straight losses in cup finals.
"We were all pretty much crying on the pitch, because it was so emotional, it was so big, it means so much to us," Klopp said.
Celebrations ran late into Saturday night in the Spanish capital and in Liverpool, as ecstatic supporters danced drunkenly in the streets and the club anthem "You'll Never Walk Alone" rang out.
By lunchtime fans began streaming back onto the streets for the parade.
- First victory since 2005 -
"We wanted to get tickets for Madrid, but obviously this is the next best thing," said Mark Hodgetts as he waited for his heroes.
"We just wanted to feel the atmosphere. We've been waiting so long — my daughter was only two when we last won it," he added.
The team returned to tabloid headlines declaring the "Joy of Six", in the Mail on Sunday, and "Six Machines", in the Sunday Mirror.
Liverpool's sixth success in Europe's top club trophy came after wins in 1977, 1978, 1981, 1984 and the memorable come-from-behind victory against AC Milan in Istanbul in 2005.
The Sunday Times hailed Klopp for introducing steely discipline into Liverpool's play this year, turning an all-out attacking team that often leaked goals into European champions.
"Game management is the biggest item Jurgen Klopp added to the armoury since desolation in last year's final in Kiev," Jonathan Northcroft said.
- Salah's redemption -
Egyptian forward Mohamed Salah, who scored a penalty awarded in the first minute for a disputed handball from Moussa Sissoko, said he had drawn on the disappointment of last year's final in which he trudged off in tears with a shoulder injury.
"Before the game, I looked at a picture of last year and we were so disappointed to lose the final," Salah said.
"I was very disappointed after that injury, I went off after 30 minutes and we lost the game. It motivated me to win today. When you know how it feels to lose, you say to yourself 'Let's go and win that'."
Liverpool's success also underlined the financial muscle of the Premier League, made rich by TV contract revenues that dwarf other European leagues.
Dutch central defender Virgil van Dijk, signed for £75 million ($95 million, 84.5 million euros), and Brazil goalkeeper Alisson Becker, a £65 million recruit, both played crucial roles in Liverpool's success.
Klopp revealed he had received a congratulatory call from Manchester City manager Pep Guardiola.
Three weeks ago, Liverpool were denied a first league title in 30 years by Abu Dhabi-backed City, despite losing just once all season.
"We promised each other already that we will kick our butts next year again," Klopp said of his conversation with Guardiola. "We will go for everything and we'll see if we get something."