At Eden Park, his "second home'' according to his nephew Alex Carpenter, about 300 mourners paid their respects to Allen, who died in Auckland at the age of 92 on Saturday.
All Black greats Sir Wilson Whineray, Sir Brian Lochore and Sir Colin Meads spoke during the two-hour service, in a large room in the stadium's North Stand, about Allen's qualities as a man and a coach.
"In the end we just wanted to play for him because we believed in what he was telling us,'' said Lochore of Allen, who coached the All Blacks 37 times for 37 wins, including 14 tests. "We believed in him as a coach.''
Allen, who served in the New Zealand Army at the Solomon Islands and Middle East during World War II, and was wounded twice during action, was known as a hard taskmaster who also had a softer side.
The tributes painted a picture of a man who believed in discipline and hard work but also someone who danced to his own tune.
That's perhaps why Sinatra's song, which followed a rousing haka by Kings College students, struck such a chord.
among the mourners were New Zealand rugby boss Steve Tew and former All Blacks Bryan Williams, Ian Kirkpatrick and Wayne Shelford.
On the casket lay a wreath of red roses, a silver fern, and an original All Blacks cap.
The other musical interlude during the service was a performance by Dave Dobbyn, who sang New Zealand anthem Loyal.
Allen will be laid to rest alongside his late wife Norma at the Auckland Memorial Cemetary in Silverdale, near his former home at Whangaparaoa, north of Auckland.
