Robert Smith did not call an ambulance nor provide even the most basic first aid as Kiesha lay dying on July 13, 2010, after being violently assaulted by her mother, Kristi Abrahams.

After the little girl died, Smith dragged her body into a western Sydney bush reserve, setting it on fire and burying it in a shallow grave.

In May 2013, former NSW Supreme Court Justice Megan Latham sentenced Smith to at least 12 years in jail for manslaughter by gross criminal negligence and accessory after the fact to murder.

But Smith elected to appeal against the severity of the sentence, firstly to the NSW Court of Criminal Appeal and, on Friday, by seeking leave to appeal to the High Court of Australia.

Smith's barrister, Philip Strickland, SC, argued on appeal that his client had been the victim of a miscarriage of justice because the courts had failed to take account of the fact that he had agreed to provide written and oral evidence against Abrahams.

When police showed Smith the evidence they had against him and encouraged him to make a statement, incriminating Abrahams, he agreed.

Justice Latham found that, because Smith repeatedly lied in his statement to police in a bid to diminish his own guilt, and because Abrahams pleaded guilty just before her trial, thus eliminating the need for him to give evidence, Smith's offer of assistance carried no weight.

The Court of Criminal Appeal essentially upheld the Supreme Court finding.

On Friday, Mr Strickland told High Court Justices Virginia Bell and Stephen Gageler that Smith's offer of assistance had been crucial because, despite its flaws, it had convinced Abrahams to plead guilty.

"The significance of the evidence can be judged by the reaction of Ms Abrahams and her legal advisers," Mr Strickland said.

"They were prepared to run a trial ... Then they get the news that the applicant [Smith] is going to provide assistance [to police]. They discuss the induced statement [by Smith] and she pleads guilty."

But Justice Bell said there was an alternative explanation for Abrahams' decision to plead guilty, namely that she had just lost an application for her trial to be heard by a judge alone rather than a judge and jury.

She also said that, even if Justice Latham and the Court of Criminal Appeal had made a legal error in the way they viewed Smith's induced statement to police, the statement was so flawed as to provide little assistance in any appeal before the full bench of the High Court.

Smith was refused leave to appeal to the High Court on the grounds that there were "insufficient prospects" that such an appeal would succeed.

The decision closes the last avenue of appeal open to Smith.

Abrahams is serving a minimum 16-year jail term for Kiesha's murder.