Adrian Donohoe, a 41-year-old father of two, was killed at Lordship Credit Union close to the Irish border on Friday night.
He was remembered as a virtuous man who was a perfect role model for the rest of society at his funeral at St Joseph's Redemptorist Church in Dundalk on Wednesday.
Chief celebrant Michael Cusack told the congregation the pain suffered by Garda Donohoe's wife Caroline - who is also a Garda - and their children Amy, who is seven, and six-year-old Niall, could not be adequately put into words.
As the service began his young son brought a football to the altar which they always played with, while his daughter came forward with the mobile phone she used to say goodnight to her father while he was on night duty.
President Michael D Higgins, Taoiseach Enda Kenny, Cardinal Sean Brady, PSNI Chief Constable Matt Baggott and other dignitaries attended the service.
Outside the church, up to 1,500 members of the public filled the streets alongside 2,500 uniformed gardaí to pay their respects.
Speaking towards the end of the service, Garda Commissioner Martin Callinan said he believes Mr Donohoe's killers will be caught.
Adrian, Detective Garda, husband, father, son, brother, colleague, community leader, GAA man, friend, we will never forget you
Martin Callinan
"No words can adequately express the great sense of loss and revulsion felt by the Donohoe family, the family of An Garda Síochána and indeed the wider public in learning about the cold blooded murder of Detective Garda Adrian Donohoe last Friday night," he said.
"We, Adrian's colleagues, are committed to ensuring that we bring the perpetrators responsible for this callous crime to justice.
"Our resolve is strengthened by the overwhelming support from the President of Ireland, the Government and members of the public."
Meanwhile a massive cross-border search operation is being conducted by Garda and PSNI officers to find those responsible.
A reward of €50,000 has been offered by the Irish League of Credit Unions for information.
A burnt-out Volkswagen Passat, thought to have been the getaway vehicle, was discovered near a forest on Cumsons Road, a back road off the main A29 from Newtownhamilton to Keady in south Armagh. It is being examined for clues.
Garda Donohoe was the first Garda to be killed in 17 years.
He died from a shot to the head while his colleague, Detective Joe Ryan, was held at gunpoint as a gang of at least four men stole €4,000.
The officer had not drawn his weapon when the robber opened fire.
Michael Cusack said Garda Donohoe was a loyal, honest, virtuous and faithful man who laid down his life for his community.
"The whole country is gutted by what has happened," he said.
Mr Cusack said the murdered detective was the perfect role model for everybody and the callous mowing down of his innocent life was a reminder that there was good and evil.
"So many people today no longer offer their services freely to the community but Adrian always did."
Garda Donohoe's coffin was taken past the station where he was based with his wife in Dundalk, before burial a mile from his home at Lordship Cemetery.