Football fans sang "wholly inappropriate and disgusting chants" about a man who died five years after a being left brain damaged outside a match.
Peterborough United and Cambridge United football clubs have both condemned the behaviour of their supporters who "let themselves down both inside and outside" the London Road stadium on Saturday.
The trouble began during the Cambridgeshire derby match in Peterborough when a section of home supporters began singing about Simon Dobbin.
Cambridge fan Mr Dobbin was permanently brain-damaged when he was attacked outside a football ground in Southend in 2015. He died in 2020 and a post-mortem examination found his death was directly linked to the assault five years before.
In a statement, Peterborough United said they condemned fans' behaviour at the weekend "in the strongest possible terms".
"We would like to unreservedly apologise to the family of Simon Dobbin and we will be working with the authorities to try and identify the culprits because those people are not 'supporters' of this football club," the club said.
Leighton Mitchell, the club's interim chief executive, added: "There is no place in society for what was chanted by a small section of co-called supporters."
Fireworks were also thrown during the match and, after the final whistle, Cambridge United fans are alleged to have caused significant damage to the Posh away stand.
The club said the damage to the toilets, offices and concourse "was on a level not seen before" and would lead to the temporary closure of the stand.
Cambridge and Peterborough are now in discussions over the cost of repairs.
A spokesman for the U's said the behaviour was unacceptable and the club had apologised to Posh.
They added: "The club also condemns the offensive chanting that came from a section of the away end which made reference towards sex offences. Songs of such nature will not be tolerated and anyone found participating will be banned from future games."
Police have opened an investigation into the criminal damage.
Both clubs have also offered their support and apologies to Mr Dobbin's widow, Nicole Dobbin.
Twelve men were jailed in 2017 for their part in the attack on Mr Dobbin, who lived in Mildenhall in Suffolk.
Although the football fan was able to return home in 2016, he was left needing 24-hour care and died in his sleep last October at the age of 48.
Seven men were arrested on suspicion of murder following his death. Three, aged 27, 30 and 46, have since been told they face no further action, while the remaining four, aged 34, 27, 39 and 29, were released under investigation.
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