Liverpool have released a statement saying they are "deeply disappointed" to hear "vile chants" regarding the Hillsborough and Heysel tragedies.
The Reds took on Premier League champions Manchester City at Anfield on Sunday.
Despite winning the game 1-0 through a Mohamed Salah strike, the Reds were furious at the away fans chanting about these tragedies during the match.
A Liverpool statement read: "We are deeply disappointed to hear vile chants relating to football stadium tragedies from the away section during today's game at Anfield. The concourse in the away section was also vandalised with graffiti of a similar nature.
"We know the impact such behaviour has on the families, survivors and all those associated with such disasters. We are working with the relevant authorities and we will also work with Manchester City in order to do our utmost to ensure these chants are eradicated from football altogether."