In its ruling, the court said it did not accept Wihongi's suggestions that matters of principle and public importance would come out of an appeal process.
"Nor are we persuaded that any miscarriage of justice arises as a result of the 12-year term imposed. The Court of Appeal's conclusion that the finite term imposed in the High Court was demonstrably too short was well open to it on the facts of this case."
The Court of Appeal last year ruled that a life sentence was not appropriate because Wihongi's mental impairment was a big factor in her offending.
The three judges said at the time, "we see this as a case of a battered defendant who has reacted in an extreme way to her abuser".
Wihongi is one of only three murderers in New Zealand who has not been given a life term.
The victim was the father of five of Wihongi's six children and the couple, who were living apart at the time of the murder, had a long history of violence towards each other. She had previously blinded him in one eye by throwing a bottle at him.
At age 13 Wihongi overdosed on pain killers, resulting in her being unable to speak or walk properly.
She suffered sexual abuse and had been involved in prostitution.
She and the victim had a tumultuous relationship, with both drinking heavily.
Before the murder, Wihongi and her ex-partner had been drinking with another man before starting to argue and shout. Their daughter, aged 11 at the time, watched her father walk out of the house and her mother get a knife from the kitchen and follow him.
Wihongi lunged at him on the path outside, stabbing him hard in the chest.
The bleeding victim and his daughter got into Wihongi's car and took off, with Wihongi following in another car.
Soon after they found the first car crashed into a fence and the driver slumped over the steering wheel semi-conscious.
Wihongi was later arrested at the accident scene.
