A total 47 people were injured, with 27 - including four children - taken to the hospital, emergency services said.
Another 20 people were treated at the scene.
Football united behind Liverpool, the most decorated men's football team in England and a world-famous brand, in an outpouring of messages over social media, including from the club's biggest rivals.
"Our thoughts are with Liverpool FC and the city of Liverpool after today's awful incident," Manchester United, historically Liverpool's fiercest opponent, posted on X.
There were similar sentiments from Everton, Liverpool's neighbour on Merseyside, which said: "Our thoughts are with all those who have been affected by this serious incident in our city."
The Premier League expressed its shock at the "appalling events" that took place at the end of the team's trophy parade that was attended by hundreds of thousands of scarf-and-flag-waving Liverpool fans.
"We have been in contact with Liverpool FC and have offered our full support following this serious incident," the league said.
On behalf of the sport's world governing body, FIFA President Gianni Infantino offered thoughts and prayers to everyone affected.
" Football stands together with Liverpool FC and all fans of the club following the horrific incident," he said in a post on X.
For all its trophies - including a record-tying 20 English top-flight titles and six European Cups - and success, Liverpool is also a club synonymous with tragedy and distress after being involved in deadly stadium disasters at Heysel and Hillsborough in the 1980s.
Liverpool's club anthem - You'll Never Walk Alone - was referenced by Kenny Dalglish, its former player and manager, in a post on social media.
"Shocked, horrified and deeply saddened about what happened at the end of the parade today," Dalglish wrote.
"Our anthem," he added, "has never felt more appropriate, You'll Never Walk Alone.
"Your Liverpool family are behind you."
Jamie Carragher, another former player and now a leading TV commentator, posted on X: "Devastating end to the day ... just pray everyone is ok."
A 53-year-old white British man has been arrested.
He was believed to be the only one involved in the incident and it was not being investigated as an act of terrorism, police said.
