Missiles were thrown at the buses as they waited in traffic.
The outside pane of the bus window was smashed, while a Jarrow supporters’ branch coach was attacked but not damaged.
Steven Pike, who helps organise the South Shields coach was with his two daughters, aged 14 and 20, and was horrified at the hooliganism.
The 47-year-old taxi driver said: “It was like going back in time to the 1970s or 80s, except then hooligans made sure they fought each other and were away from the crowds.
“This was a coach which was mostly filled with teenagers. We stopped at a red light and loads of kids were outside the coach – they started throwing bricks and even a scaffolding pole at the bus.
“One pane was smashed – thankfully just the outside one, and some were trying to get on.
“Who knows what would have happened if they did. All I could think about was trying to keep my girls safe.”
A spokesman for Merseyside Police said: “We can confirm that we have now received a single report of damage to a football supporters’ coach leaving the Anfield area.
“A driver of one of the coaches called the force yesterday to say that a window had been smashed by an object thrown from outside a chip shop on Stanley Park Avenue South.
“Enquiries will be now carried out.”