An Auckland mother whose partner bashed their baby to death says she cannot forgive herself but hopes her baby gazes down on her from heaven with pride one day.

The child's mother addressed the High Court in Auckland today, through a detective who read her victim impact statement aloud.

The baby was killed last year during a Covid-19 lockdown when the father, on bail at the time for assaulting his partner, repeatedly bashed the child in the head.

He pleaded guilty to manslaughter and was today sentenced to six years and six months in jail.

The father, mother, and their child cannot be named and the father has interim name suppression.

"I am filled with regret from the day my baby left the world," the young mother said in her statement.

"I could never have thought [he] could do something to hurt our kids. I can't forgive myself."

She said she regretted leaving the child with the father, who later lied about the child's death.

"I knew inside my heart he was not telling me the truth."

The mother said she saw "disgusting marks" on her dead baby's head.

"He brought her into the world with me. How could he take her away from it?"

She said she wanted the father to take responsibility for what he did.

"He took our baby away and he has to pay for that."

But she added: "I have been judged this entire year by people who don't know the facts. I am finally starting to move on."

She said she had quit drinking, found employment, and hoped the baby was looking down on her from heaven and could be proud of her.

"I miss my baby every day."

Crown prosecutor Jasper Rhodes said the father had care of the baby for only minutes before launching his attack.

"Here, we're talking about multiple intentional blows to the head...How he would punch an adult in a boxing match."

Rhodes said the father could not use the stress of childcare or a crying baby as an excuse.

"He had other options available to him. He was on bail conditions to reside at a different address."

Rhodes accepted the father was remorseful now.

Defence counsel Marie Dyhrberg QC said the father was not trying to evade responsibility, and had started rehab courses in prison.

The father had been a weekly methamphetamine user but had more recently taken anger management and drug and alcohol treatment courses.

"In no way was he delaying or trying to put the blame on anyone else."

"He was obviously a grieving father as well," Dyhrberg added.

"He had to himself come to a point where responsibly and ethically and legally he did accept this."

Justice Kit Toogood said the attacker misled ambulance officers after the baby was attacked.

Paramedics were told the South Auckland baby had flu-like symptoms.

"Tragically, she was virtually deceased by the time they arrived. There was no hope for her," the judge said.

"Her death was initially treated as a potential Covid-19 case."

But a pathologist found evidence of brain bleeding from a historic post-birth injury.

That made her especially susceptible to catastrophic damage from head injuries, the judge added.

Justice Toogood said the man exaggerated his drinking and drug use but had genuine problems with abandonment and exposure to gang lifestyles when younger.

The father at one point claimed he was coming down from a meth binge when he attacked the baby.

"You should consider yourself very fortunate that you are not being sentenced for murder," the judge told the killer.