Nine people were arrested as Liverpool fans ignored police advice and crowded the streets following the club’s trophy-lifting final home game.
Police had issued a dispersal order to clear about 3,000 fans from Anfield.
Nine arrests were made on suspicion of being drunk and disorderly, drink and drug driving, affray and assault.
The club said in a statement it was “disappointed” with the scenes outside Anfield overnight and with supporters who “did not heed the celebrate at home advice”.
It thanked supporters who stayed at home “protecting their loved ones and our city” from the “threat of this pandemic” as well as those who helped clean up Anfield after large crowds gathered around the stadium.
The Mayor of Liverpool Joe Anderson has also tweeted his thanks to those involved in the clean-up operation.
The dispersal order had been set up to try to prevent a repeat of the widespread gatherings seen last month, when Liverpool clinched their first Premier League title.
Merseyside Police said the order was put in place at 21:30 BST “following increased numbers of people gathering near the ground”.
The imposition of a dispersal order gives police the power to direct people suspected of causing crime, or those seen as likely to cause crime, nuisance or anti-social behaviour, to leave an area for up to 48 hours.
Liverpool manager Jurgen Klopp, captain Jordan Henderson and former player and manager Dalglish had called on fans to stay away because of the risk of spreading coronavirus.
Assistant Chief Constable Natalie Perischine, from Merseyside Police, said “the vast majority of the crowd were good natured and had dispersed by 02:00 BST”.
“Thankfully we didn’t see the sort of incidents of disorder and criminal damage we saw at the Pier Head on 27 June, the investigation into which has seen more than 20 arrests made to date,” she added.
“We would like to thank the overwhelming majority of Liverpool fans who listened to that advice and celebrated their team’s success at home,” she said.
The club previously condemned the behaviour of some fans in the days after the title was secured on 25 June.
Thirty-four people were injured – three seriously – as thousands of people congregated at the city’s waterfront despite coronavirus restrictions, while other celebrations were held outside Anfield and in the city centre.