The decision states Brown's lawyer Fiona Guy-Kidd appealed against his conviction, arguing that a miscarriage of justice occurred at his trial on three occasions.
She believed illegitimate and prejudicial propensity evidence was given by a family member of Brown about his tendency to "rage".
The declining of the judge to warn the jury about the reliability of the evidence from a 16-year-old woman who was involved in the incident was also highlighted by Kidd.
She said her client argued the woman had a motive to give false evidence about him because she hoped to get a reduction on her sentence at appeal in recognition of her assistance in giving evidence for the Crown.
The last point of the appeal was a letter from the same woman to Brown from prison - she wrote to him saying she had told lies at the trial.
In his decision, Justice Gilbert states the comments from the family member were irrelevant and he was not persuaded that there was "any real risk of a miscarriage of justice having occurred on this ground".
About the lack of warning from the judge, Justice Gilbert states the decision to decline to give a reliability warning about the woman's evidence was adequate and he did not consider there was any real risk the outcome of the trial was affected.
Justice Gilbert also dismissed the appeal about the letter, saying the woman confirmed the contents of her affidavit at the hearing of the appeal and was cross-examined on it.
"We accept her explanation for making the statements in her letter to Mr Brown — she felt responsible for the events that unfolded and wished to assist Mr Brown with his conviction appeal."
Brown and six other people were charged in relation to the murder of McAllister. Brayden Whiting-Roff pleaded guilty to murder shortly before the trial and was sentenced to life imprisonment and ordered to serve a minimum period of 12 years and six months.
The 16-year-old woman pleaded guilty to being a party to McAllister's murder four months prior to the trial and agreed to give evidence for the Crown. She was sentenced to life imprisonment and ordered to serve a minimum period of 10 years.
Laura Scheepers was sentenced to 12 months' home detention after being found guilty of manslaughter. The remaining three defendants were found not guilty during the trial.