Mr Black, 52, was killed by suspected dissident republicans in a high-speed shooting on a motorway as he drove to work at Maghaberry Prison, Co Antrim on Thursday. He is the first prison warder killed by paramilitaries in the North in 20 years.
His daughter Kyra, 17, paid tribute to her “special hero” but the extended family of the father-of-two said they hoped the perpetrators would “get what they deserve”.
Dr Roy Patton, head of the Presbyterian Church in Ireland, vowed the efforts of the gunmen to drag Northern Ireland backwards would not work.
Smartly-uniformed prison officers carried the coffin to Molesworth Presbyterian Church in Mid Ulster in military fashion.
Stormont first minister Peter Robinson, PSNI chief constable Matt Baggott, and justice ministers north and south of the border attended the funeral in Cookstown, Co Tyrone.
Mr Black’s cousin Jim Slaine told mourners: “The people who did this to David are cowards to the extreme. They have probably never done a decent day’s living, unlike the man they killed. We all hope that the perpetrators get what they deserve in life but we all know they will have to live with what they have done and they will meet their maker.”
The funeral of Mr Black, who had more than 30 years’ service, was attended by thousands of people.
His son Kyle, 20, also had a message for the gunmen: “They can take daddy from us... they can deprive mummy of a loving husband, but they can never take away the love that we have in our hearts and the memories that we will all cherish for the rest of our lives.”