An image shows damage to a window – which the club said was caused by an object being thrown at the bus.
Liverpool were fined in 2018 after fans attacked the City bus as it arrived at Anfield for a Champions League game.
Manchester City manager Pep Guardiola has also said opposing fans threw coins at him during Sunday’s match but that he wasn’t hit.
Liverpool, meanwhile, condemned “vile chants relating to football stadium tragedies” from the away supporters’ end during the game.
Graffiti was also left in parts of the Anfield Road End, referring to “murderers” and the number of people killed at the Heysel and Hillsborough disasters.
Liverpool flipped the form book on its head by winning 1-0 thanks to a Mo Salah goal, while City had a goal disallowed.