"In the result, we consider that the end sentence of seven years six months imprisonment was fully justified.''
They found that Judge Gibson had given a "generous discount'' for the woman's guilty plea
The woman's lawyer Lorraine Smith had said her client had been abused and that explained or influenced the abuse. She also said her client had a previously clean record.
But the Justices said it was artificial to talk of a person's previous good character in cases where there has been a "sustained period of abuse'' directed at young children.
They also addressed the abuse against the woman herself.
" ... We consider that the nature of the appellant's offending is so bad that no account can be taken of this personal circumstance.''
The case sparked a Ministerial inquiry conducted by former ombudsman Mel Smith. It looked at the girl's case and other matters relating to the welfare and protection of children.
It included 13 recommendations.
They include better information sharing, new Child Youth and Family workers for schools, mandatory reporting of abuse and neglect, urgent research on kinship care, and a new Child Protection Court.
During sentencing Judge Gibson said the police summary of facts made "horrific reading''.
"This is a long, sad story of a litany of abuse on a young child at the hands of her mother.''
Shortly after the girl's birth she was removed from her mother's care by Child Youth and Family because of concerns about neglect and abuse.
The girl was was returned to her mother in 2008.
Judge Gibson said the girl was slapped on her face and body after allegedly showing signs of "sexual behaviour'' towards her brother. She also used weapons including a hammer, machete and steel pole to beat her daughter.
The abuse was not only physical but included the mother writing words on the girl including "skank'' and "incest''.
When police raided the mother's house in November last year, they found the girl dehydrated and starving. She had been hidden in a wardrobe in the hope police would not find her.
"This is one of the most appalling cases the courts have had to deal with.''