Murphy collapsed and died suddenly on Friday (8 August), aged 86, after being cast as Ser Denys Mallister, the oldest member of the Night's Watch.
He was set to shoot further scenes and had told friends of his excitement to be part of the cult TV show, the fifth season of which is currently being filmed in his home country.
Game of Thrones creators D.B. Weiss and David Benioff told The Independent: “We will not be recasting J.J. Murphy.
"He was a lovely man, and the best Denys Mallister we could have hoped for. And now his watch is ended."
Mourners gathered at St Brigid’s Church were given a moving sermon on the active role he also played as the life and soul of the parish.
"He was delighted to be cast for a part in the fantasy epic Game of Thrones - but now all fantasy is left behind," Fr Edward O'Donnell said.
"As JJ fell asleep in this world, it is our Christian hope that he wakened in eternal life, and entered into reality beyond reality, and that he stands now before the throne of the one before whom 'every knee shall bow'."
The actor and his wife, Mary, were set to celebrate their 59th wedding anniversary next month.
They had raised £167,000 in charitable donations for orphans in Bosnia, too.
Murphy was also due to appear in high budget vampire film Dracula Untold, directed by Gary Shore. In it, he played the role of a village elder.
His other film credits include Mickybo and Me, Cal and Angela's Ashes. However, he was best known for his work on the stage, having trained with the Ulster Group Theatre School in 1948.
Murphy, a long-standing member of actor’s union Equity, also worked for years at the Lyric Theatre in Belfast, where he helped to hone the crafts of renowned actors such as Ciaran Hinds and Liam Neeson.
"His passion for theatre, for the welfare and betterment of actors and those who worked in the performing arts was always there," actress and fellow Equity member Maggie Cronin said in tribute. "It was an integral part of the man."
Meanwhile, Murphy’s agent Philip Young told of his heartbreak on hearing the news that the "wonderful"actor had passed away.
“I have never encountered a man with more spirit, passion and love for his craft,” he said.
Young said that a number of messages of sympathy from HBO executives.
Murphy is survived by his wife Mary , his two children Joseph and Jane, and a granddaughter, Sarah-Jane.