They were first reported missing by family members before police found their bodies a few days later.
Martin Hone already pleaded guilty to the men's murders and was sentenced to life with a minimum non-parole period of 20 years.
Pulemoana entered an appeal to the Court of Appeal on January 31, but it was dismissed in Justice Moore's judgment released today.
The appeal considered three things.
The first was whether a Crown witness gave evidence resulting in a miscarriage of justice.
Justice Moore concluded there was nothing deliberate or improper about the way it was introduced.
The second was whether a juror should have been discharged, but Justice Moore deemed the juror impartial.
The third consideration was whether a murder conviction was unreasonable for Pulemoana. Justice Moore concluded it was appropriate.
Pulemoana stood trial with co-accused Mikaere James Hura, 21, who was found guilty of the manslaughter of both men and was jailed for six years.
Zen Pulemoana (right) and Mikaere James Hura appearing in the High Court at Rotorua. Photo / FileRichard Te Kani pleaded guilty to manslaughter and is serving a sentence of 15 years in jail.
He also entered an appeal this year.