Lord Chief Justice Lord Thomas, Mr Justice Silber and Mr Justice Globe said the personal statement of Mr Greaves's widow Maureen made clear the devastating effect the murder had on her and the rest of the family.
Lord Thomas said they agreed with the trial judge's assessment that although Bowling may not have intended to kill, the brutality of the attack and the force he used showed he was entirely indifferent to the risk that he might.
"There was recklessness of the highest degree."
He said they were satisfied the aggravating factors in the case would have set the minimum term to one in excess of 30 years had there not been a guilty plea.
"In our judgment, the judge came to the perfectly correct conclusion," said Lord Thomas.
He added: "This was without doubt a vicious, pre-planned attack on a vulnerable man using a weapon and on a Christmas Eve.
"His plea of guilty was his only mitigation.
"We have no doubt whatever that the minimum term of 25 years less time on remand was entirely appropriate, would safeguard the public and ensure there was just punishment and retribution for this terrible crime.
"There is no basis whatsoever for this application."
A man who battered a church organist to death as he walked to Midnight Mass in Sheffield has lost his appeal against his minimum 25-year sentence.
Jonathan Bowling was jailed for life at Sheffield Crown Court last July for the murder of lay preacher Alan Greaves, 68.
Bowling, 22, battered devout Christian Mr Greaves around the head with a pick-axe handle as the pensioner walked to play the organ for Midnight Mass at St Saviour's Church in High Green on December 24, 2012.
The father-of-four suffered catastrophic head injuries and died three days later in hospital.
The widow of a church organist murdered last Christmas says she'll be back at the scene of the attack this Christmas Eve. Alan Greaves was beaten to death while on his way to midnight mass at High Green near Sheffield.
Today as she unveiled a plaque in his memory Maureen revealed plans to hold midnight mass this year at the scene of her husband's murder. She says it'll be a chance to celebrate his life. Chris Kiddey reports.
The widow of church organist Alan Greaves today came face to face with his murderer and heard him admit - for the first time - that he'd carried out the Christmas Eve killing.
Maureen Greaves was at Sheffield Crown Court today when Jonathan Bowling pleaded guilty to her 68 year old husband's murder. A second man has denied the charge and he will now face a trial by jury. Ben Erlam reports.
One of two men accused of murdering the church organist Alan Greaves has admitted his guilt today. His co-accused has pleaded not guilty and the case will go to trial later this month. David Hirst reports from Sheffield Crown Court.
A 22-year-old man admitted the murder of church organist Alan Greaves when he appeared before Sheffield Crown Court today. Jonathan Bowling, from Burngreave, pleaded guilty during a short hearing.
His co-accused, Ashley Foster, 21, who is from High Green, appeared via a video link and he denied the murder of Mr. Greaves. The case will go before a jury on June the 24th and is expected to last for at least two weeks.
Mr. Greaves' family were in the public gallery during today's hearing. The former social worker was attacked on his way to play the organ at midnight mass at St Saviour's Church at High Green.