Merseyside Police introduced a 48-hour dispersal zone around the ground during the club’s match against Chelsea on Wednesday night but the force said only nine arrests were made, despite large numbers of supporters congregating outside the Kop end.
Ahead of the match, the club, council, police and supporters’ group Spirit of Shankly had urged people to celebrate from their homes.
Former player and manager Sir Kenny Dalglish tweeted: “Can everyone please respect the guidelines and enjoy the moment.
“This is a dress rehearsal for when we can all celebrate together safely.”
But supporters continued to arrive at the ground through the evening.
There were no fans inside the ground as the trophy presentation was made, but outside, in Walton Breck Road, crowds erupted into huge cheers as fireworks went off over Anfield.
Fireworks were also set off in the street, along with flares, and fans waved flags and sang as they celebrated into the early hours.
Police officers, who stood in cordons across the road, took flares from some fans but did not stop them joining the crowd.
A spokeswoman for Merseyside Police said nine arrests were made throughout the night, mainly for drunk and disorderly and drink- or drug-driving offences, with three for affray or disorder.
The force said the dispersal zone, which allowed officers to ask those they suspected would cause crime or anti-social behaviour to leave the area, was set up in anticipation of large crowds following earlier incidents.
Thousands of supporters celebrated outside Anfield last month when the team’s first top-flight title in 30 years was confirmed and huge numbers gathered at the city’s Pier Head the following night, where police reported violent confrontations.
