On 3 November, Butt, 27, was sentenced to two and a half years in prison and promising pacer Mohammad Amir, 19, was ordered to serve six months in a young offenders' institution.
In a scandal that shook the sport, the pair, along with their team-mate Mohammad Asif and their agent Mazhar Majeed were imprisoned for their roles in fixing parts of Lord's Test against England last year.
Butt's father Zulfiqar said he had hoped for judicial relief.
'I have just heard about the appeal's rejection,' he told AFP. 'We thought that some leniency would be granted but the rejection of appeal is disappointing and now we see no way of getting any relief.'
Butt's lawyer Ali Bajwa had argued that the former captain's sentence was 'out of proportion to the seriousness of the offence that was committed.'
Bajwa described Butt as a broken man in a state of 'ruin and disgrace,' adding that the 'very fact of conviction and imprisonment amounted to exceptional punishment' for him.
His wife had given birth to a baby boy just 30 minutes before the trial verdict.
Amir's lawyer Henry Blaxland had urged the judges to impose a suspended sentence of a length that would enable his immediate release.
Zulfiqar said he hopes to visit his son at the earliest opportunity, but added that it was 'difficult arranging all travel documents so quickly.'
He said he had spoken to his son just once since the sentencing.
'It's difficult to get through to him, but we have talked just once and the time was barely enough to discuss how he is doing,' Zulfiqar said of the phone conservation last week.
Amir's mentor Asif Bajwa also said he was disappointed with the appeal's rejection.
'I expected something better to come out for him, but it has been disappointing throughout. A whole year has passed in dejection and emotional set back,' he told AFP.
