Steven Bennett and Suni Gill are on trial accused of the murder of Anthony Bird who suffered fatal injuries when he was kicked and punched during an incident in Victoria Park, in Tipton, on July 26 last year.
Mr Bird, 50, was an alcoholic who was suffering from cirrhosis of the liver at the time.
Prosecuting counsel Mr Adam Birkby told Wolverhampton Crown Court: "A pair of grey trainers seized from Steven Bennett's home were analysed and blood staining found on the under side of the sole.
"The DNA profile of the blood matched the DNA of Anthony Bird."
He said that when Bennett, 38, was arrested on suspicion of murder on August 20 last year he told officers, "you have got the wrong man".
Mr Birkby told the court that when Bennett was again interviewed at Oldbury Police Station the following day he denied killing Mr Bird in a prepared statement, in which he also stated that he was "wrongly identified" by a member of the public who had told officers that he was the "white male involved in the assault".
He told the jury that Gill, 33, also provided a prepared statement, in which he stated: "I confirm that I deny the allegation of murder made against me. I have not committed this offence.
"I have nothing further to add."
The jury previously heard that the pair had allegedly subjected the older man, who they did not know, to a prolonged brutal and ferocious beating during which the rained kicks and punches to his head and body, after accusing him of being a “paedophile”, an unsubstantiated claim.
Mr Bird suffered fractures including to his jaw and cheekbones along with bruising as a result of what happened to him in the Victoria Road park.
He was declared dead in hospital at 8.30pm on August 12.
A post mortem report concluded that Mr Bird, who lived in the area, died as a result of blunt force head impact with a background of serious pre-existing liver disease.
Bennett, of Bevan Road, and Gill, of Shore Road, both in Tipton, both murder and deny causing grievous bodily harm with intent.
The jury heard both accepted being in the park on the day, however, Bennett claimed to only punched Mr Bird once, while Gill claimed he was drunk and had mental challenges.
The trial continues.