A video emerged online showing Pep Guardiola's squad celebrating their Premier League title win on a team plane, adopting a Reds chant which has been made famous over the past season.
City officials have insisted that any suggestion the song relates to either the Hillsborough or Sean Cox tragedy is "entirely without foundation" and the players were, in fact, referring to the 2018 Champions League final in Kiev between Real Madrid and Liverpool.
However, Sean Cox's brother Martin has condemned the "inappropriate" chant which has hit close to home for a family still dealing with grief.
“My first reaction was I was very disappointed,” Martin told TalkSport on Wednesday.
“It’s so close to home for ourselves with Sean, so we’re shocked now, to be honest with you.
“Any song like that, these players are media trained in this day and age and are role models for children.
“I don’t understand why the first thing they want to do, right after they win the league title, is sing about Liverpool, first of all, and then actually sing about fans getting battered in the streets.
“Surely they know that the song is inappropriate.”
City successfully defended their Premier League crown on Sunday, beating Brighton 4-1 to finish the 2018-19 campaign one point ahead of Liverpool.
The two clubs have been involved in a thrilling title race over the last 10 months, with the Reds just falling short despite an impressive 97 points haul.
Cox added: "I don’t understand why Man City win the league and want to sing about Liverpool. They should be singing about their own club, concentrating on their own team.”
Martin's brother Sean sustained brain injuries and spent months in hospital after he was assaulted before Liverpool played Roma in a Champions League semi-final in April 2018.
Sean left a rehabilitation centre earlier this year and Martin also offered an update on his recovery: "Sean is doing good. He’s progressing, which is the most important thing.
"He’s still on a massive long road ahead, but he is progressing. Slowly but surely, he’s getting there.
“It’s baby steps at the moment but we’re on the right road.”