The Garda Commissioner has asked that Colm Horkan be remembered for the way he lived his life, rather than how he died.
The 49-year-old Mayo native was laid to rest on Sunday in Charlestown, days after he was shot dead in Castlerea where he was based as a detective.
Stephen Silver, of Aughaward, Foxford, appeared in court last Friday charged with the murder of Detective Horkan.
He is due back in court via video link later this week after being remanded to Castlerea prison.
Speaking at the funeral mass, Commissioner Drew Harris said gardaí have been overwhelmed by the support shown to them since Detective Horkan's death.