A report on St Petersburg’s Peter TV channel said that on the night prior to the game that a 40-strong group had attacked travelling fans as they emerged from a bar in the city.
Liverpool supporters were forced to take shelter inside before security staff used baseball bats to disperse the attackers. Local media reports said nobody was seriously injured in the incident.
Supporters also said they had been attacked on metro trains as they travelled to and from the Petrovsky Stadium, with some also claiming to have been attacked inside the ground.
The Zenit fans have been under the spotlight of late after sections claimed that the club should employ no homosexual or black players in the squad.
Brendan Rodgers had commended the home support for their behaviour during the game and thanked them for a warm welcome.