She said she "will not engage with those conducting this vicious campaign."
She said she had reported on the reasons for her resignation to the Home Secretary and a select committee in the UK.
"The conduct and failures of those involved has since come under scrutiny. This will give New Zealanders some insight into what I experienced."
The Times reported Dame Lowell's lawyers had denied their client had made any derogatory remarks or had treated junior staff with contempt, saying she had very little contact with them.
The Times had claimed Home Office officials covered up the allegations.
They are the latest allegations to surface against Dame Lowell, who previously faced scrutiny about her understanding of English law, long periods of leave and her generous pay.
A spokeswoman for Prime Minister John Key declined to comment.
A spokeswoman for Attorney General Chris Finlayson said Goddard had resigned from the judiciary when she took up the role in the United Kingdom and was no longer a judge.
"Questions relating to the Independent Inquiry into Child Sexual Abuse in England and Wales are a matter for the UK Government and the Attorney-General has no comment."
Dame Lowell was appointed to the role of chair of the Independent Inquiry into Child Sexual Abuse in March 2015 by then Home Secretary Theresa May.
The Times said the Home Office had wanted a Commonwealth person to head the inquiry after the two previous British chairs resigned because of the possibility of conflicts of interest.
In Goddard's statement said she had given up her role as a judge in New Zealand at the "urgent request" of the British Government.
The inquiry was established in 2014 following allegations of a paedophile ring operating within Westminister in the 1980s. It is investigating whether public institutions, from churches to Government institutions, failed to protect children from abuse.
Dame Lowell resigned after 16 months in August, telling the Home Affairs Committee the inquiry had a "legacy of failure," was too broad and not well resourced enough, and that the staff were inexperienced.
"I felt as chair handicapped by not being given a free hand to recruit staff of the type that I judged to be essential."
Her salary of $640,000 plus $200,000 in entitlements made her one of Britain's highest-paid public servants.
It was revealed that she had spent 30 days on leave in her first year in the job, and 44 days in Australia, where she held just two meetings with members of a child abuse inquiry there.
Dame Lowell defended her handling of the inquiry after her resignation, telling the Home Affairs Committee that in her 16 months as chair it had dominated her life.
"I made a firm commitment to undertake it and was determined to see it through to its conclusion. I am disappointed that this has not been possible.
"However, I am pleased I was able to set it on its way. Ultimately however I had to face a situation which I could not solve and which would continue unless challenged.
"I resigned to make that challenge occur."
Dame Lowell was replaced by Professor Alexis Jay, who previously carried out a child sexual exploitation inquiry in Rotherham.
