Following Everton’s victory over Crystal Palace, seven individuals were detained for disturbance outside Goodison Park.
Merseyside Police said a large group threw bricks and bottles at a police car on County Road in Liverpool at around 23:15 BST on Thursday.
Before the mob dispersed, two more police vehicles were damaged.
Although no one was badly injured, Ch Insp Jim Wilde said the “despicable behavior” meant that important vehicles would have to be taken off the road until they were repaired.
According to police, five males were detained on suspicion of being drunk and disorderly in a public place, and one was arrested on suspicion of assaulting an officer while on duty.
They were later released and will face charges at a later time.
After two beer bottles were hurled at cops, a 26-year-old male from Bootle was detained on suspicion of violent disorder.
He was transferred to a Merseyside police station and is still being held.
“We know the great majority of the community would be outraged to learn that damage was done to emergency vehicles while our officers were attempting to keep the peace and keep people safe,” Ch Insp Wilde said.
“As a result of this terrible behavior, two essential vehicles were forced off the road and will now need to be repaired.”
According to him, their withdrawal from duty had a “clear impact” on officers’ capacity to respond to situations.
He wanted anybody who saw the chaos on County Road to come forward.
Everton fought back from a two-goal deficit to defeat Crystal Palace 3-2, avoiding relegation from the Premier League.
During a pitch invasion when fans poured on to the pitch at full-time, Crystal Palace manager Patrick Vieira got into a fight with an Everton supporter.