Manchester City and Liverpool have condemned the "unacceptable" scenes that marred the teams' EFL Cup tie, with the Greater Manchester Police (GMP) investigating several incidents in the aftermath of Thursday's game.

EFL Cup holders Liverpool fell to a last-16 exit at the Etihad Stadium as goals from Erling Haaland, Riyad Mahrez and Nathan Ake fired City to a 3-2 win in their first game after the World Cup.

Prior to the match, the two rivals released a joint statement with the aim of easing mounting tensions between the clubs.

Their Premier League clash in October – in which Liverpool claimed a 1-0 win – saw coins thrown at City boss Pep Guardiola by Reds fans, while City supporters could be heard singing songs related to the Hillsborough disaster, in which 97 Liverpool fans were unlawfully killed in 1989.

On Friday, a GMP statement said several incidents which took place on Thursday – including one that left a 15-year-old girl with head injuries – were being investigated.

GMP's match commander Superintendent Gareth Parkin said: "We are aware of a number of objects, including coins and a smoke bomb, that were thrown during the match. We will be investigating the incidents and reviewing CCTV from the night.

"Clearly, throwing objects in a confined area can be dangerous and have serious and sometimes devastating consequences – GMP sends its thoughts and wishes to the girl who was injured and wish her a speedy recovery."

The statement added two men had been arrested on suspicion of trying to take pyrotechnics into the stadium, while another man was arrested for a racially aggravated public order offence.

Another incident saw a 53-year-old man assaulted after the game, causing him to require hospital treatment.

Responding to the unrest, the two clubs pledged to "eradicate" such behaviour while praising the conduct of the majority of supporters.

A joint statement read: "Liverpool FC, Manchester City FC and the chairs from our supporter groups have worked together in recent weeks to remind fans of our expectations and both clubs would like to thank the vast majority of fans for their behaviour at last night's Carabao Cup match at the Etihad Stadium.

"It is, however, hugely disappointing that there were a number of incidents during last night's match that are wholly unacceptable.

"These incidents will be fully investigated, reported to the police and the individuals who are found to be responsible will be subject to the sanction process of their respective club.

"Liverpool FC and Manchester City FC are fully committed to working together to eradicate these issues from our fixtures. They have no place in football."