Fr Chesney, who died from cancer, aged 46, in 1980, was never questioned by police despite being suspected of involvement in the atrocity.
Last week, a report by Northern Ireland Police Ombudsman Al Hutchinson revealed that the RUC investigation into the atrocity was "compromised" after senior officers conspired with the Government and Church to protect him.
Writing in the Irish News, Bishop Daly, who was in charge of the Derry diocese between 1974 and 1993, hit out at the media for not questioning "key aspects of the Ombudsman report".
"I find media coverage of the Claudy Report very disquieting. Media have not questioned key aspects of the Ombudsman's Report in relation to allegations that Fr James Chesney was a senior IRA figure directly linked to the bombings," Bishop Daly said.
"The once sacrosanct presumption of innocence has been dispensed with and replaced with a presumption of guilt."
After the atrocity, Fr Chesney was called in for questioning by the-then Bishop of Derry Neil Farren and his successor, Edward Daly, and denied any involvement in the attack.
He was transferred to a parish in Co Donegal, outside the Northern Ireland jurisdiction in 1973, following secret talks between then Secretary of State William Whitelaw and the head of the Catholic Church in Ireland, Cardinal William Conway.
"I am not at all convinced that Father Chesney was involved in the Claudy bombings", Bishop Daly writes.
"I may be mistaken, but I do not think so. I was a contemporary of his at school. I did not know him very well but knew him reasonably well.
"I have seen convictions based on signed admissions and forensic evidence completely overturned years later. Fr Chesney was never arrested, questioned, charged or convicted. He cannot answer for himself. He has been dead 30 years."
At the time, senior politicians feared the arrest of a priest in connection with the atrocity could destabilise the security situation even further.
The 1972 Claudy bombing occurred six months after Bloody Sunday on the bloodiest month of the bloodiest year of the Troubles.
"It is a huge insult to suggest I would knowingly allow someone whom I knew to be a mass murderer to serve as a priest in my diocese", Bishop Daly writes.
"I do not accept theories - voiced by several people in the aftermath of the Report - about priests being endangered and a possible subsequent fall-out in society if Fr Chesney had been arrested."
According to intelligence reports, detectives believed Fr Chesney was the IRA's director of operations in south Derry.
Last week, Mr Hutchinson also revealed that the police had intelligence suggesting that Fr Chesney continued to be involved in the IRA after the Claudy bombing.
Bishop Daly says he does not accept the Ombudsman's suggestion "that Fr Chesney continued his republican activities when he was in Donegal."
"As bishop at that time, I was aware of his previous espousal of views, and he knew I was having him observed. There was a never a complaint about him."
Last week, Cardinal Sean Brady denied that the Catholic Church covered up the activities of Father Chesney
"The Claudy dead and wounded and their relatives deserve both truth and justice", Bishop Daly wrote in the Irish News.
"They were also cruelly deceived by senior RUC figures and the Northern Ireland Secretary in the failure to ensure that the bombing was thoroughly investigated."
Last week, Secretary of State Owen Paterson apologised to the Claudy families on behalf of the UK Government.
Nine people were killed and 30 were injured in the Co Londonderry village when three car bombs exploded in quick succession on 31 July 1972.