Aloysius Hackett, 60, was found dead in the back yard of his family home on the Aghindarragh Road, near Clogher on Friday night.
His funeral took place at St McCartan's Church in Augher at noon on Wednesday.
Mr Hackett's 18-year-old son, Sean, initially denied involvement in the murder, but later told police: "I did it. I shot him."
He appeared at Omagh Magistrates' Court on Tuesday, when a court heard the teen suffered from depression.
Sean Hackett, who captained last season's Tyrone minor Gaelic football team, was granted compassionate bail on the condition that he was accompanied at all times by his lawyer and Tyrone Gaelic football manager Mickey Harte.
He was also banned from speaking to anyone else, including family members.
He was escorted back to Hydebank Young Offenders Centre after the funeral.