Liverpool FC has condemned the behaviour of some fans who gathered in the city to celebrate the Premier League title win as “wholly unacceptable”.
Flares were lit as thousands turned up at Pier Head waterfront despite restrictions on gatherings.
Firefighters also extinguished a small fire at the landmark Liver Building.
Mayor Joe Anderson said the events “brought Liverpool Football Club and the city of Liverpool into disrepute”.
Fifteen people were arrested later in the evening for violent disorder and police officers were “subjected to a number of violent confrontations”, Merseyside Police Chief Constable Andy Cooke said on Twitter.
“Last night, children and families were present alongside others and heavy-handed police intervention was therefore not appropriate at the time,” he said
Assistant Chief Constable Jon Roy said missiles were thrown at police, including at two officers who were trying to help the victim of an assault and make an arrest.
“Both those officers came under attack from bottles being thrown at them and were injured as a result,” he added.
Mersey Fire said it quickly extinguished a small blaze on a first floor balcony of the Liver Building thought to have been started by a firework.
A joint statement from Liverpool FC, the city’s council and Merseyside Police said: “Our city is still in a public health crisis and this behaviour is wholly unacceptable.
“The potential danger of a second peak of Covid-19 still exists and we need to work together to make sure we don’t undo everything that has been achieved as a region during lockdown.
“When it is safe to do so, we will all work together to arrange a victory parade when everyone can come together to celebrate.”
Mr Anderson told BBC Radio Merseyside he was “frustrated and angry and upset”.
He said: “People were urinating in doorways of the Cunard building because people gathered there with cases and cases of beer.
“About 95% of fans have behaved remarkably well, brilliantly, and listened to our pleas not to gather together, and yet there are a tiny minority besmirching Liverpool Football Club’s name.”
Friday was the second consecutive night that crowds gathered to celebrate the club’s first league win in 30 years.
“On Thursday, when they gathered outside Anfield, you could argue that the passion was there and we had to accept that was inevitable,” Mr Anderson said.
“But what we saw yesterday was pre-meditated, planned, thought through, and drink played a major part in that.
“That’s no [longer] acceptable now in this city.”
At the scene
Philip Munns, BBC Radio Merseyside
It just looks absolutely horrendous.
You’ve got boxes, broken bottles, cans, empty gas canisters, loads of bags all strewn across the lawn area in front of the Liver Building and by the Mersey Ferry Terminal.
Normally, many people will go down on a daily basis and it’s an absolutely spotless beauty spot, but that’s not the case this morning.
The clean-up is already under way.
After Friday’s crowds, Merseyside Police issued a dispersal order for the city centre until Sunday.
“We know a lot of Liverpool fans want to celebrate their Premier League win, but there is a time and a place for this – and this weekend is neither,” a spokesperson said.
Mr Anderson said he would talk to police about “why no action was taken much earlier”.
“I’m expecting Merseyside Police to come down really heavy now… it’s about the safety of our city,” he said.
“I am angry that people are not considerate to other people, their families, the NHS and the workers that have to deal with this. Covid has not gone away.”
He said reported cases of coronavirus had fallen in the past weeks but crowds were “putting that at risk”.