"We are determined to improve on this rating next quarter, when our results will more accurately reflect on our performance," the UK-headquartered multinational said.
"Our contract sets clear performance standards, expects us to achieve significant savings for government, and holds us accountable if we don't deliver."
Serco lost its contract to run Mt Eden remand jail after resisting attempts by Corrections to improve poor supervision and understaffing.
The Mt Eden fightclub scandal last year plunged the facility Eden from the top of the prison performance tables to the bottom overnight - and until now Corrections had not released an updated table, saying it was revising how it compiled them.
In announcing its prison expansion last week, the government made no mention of Serco or other private operators - though a public-private partnership will build and maintain a revamped Waikeria Prison in Waikato, adding 1500 beds, which Corrections will run.
Claims private prisons more efficient unproven - Australian report
Australia has nine private prisons - three run by Serco - and the highest rate of private incarceration per capita in the world.
A University of Sydney Business School report has concluded that claims private prisons are more efficient and better performing than public prisons hadn't been proved.
The Sydney study is the latest to question how commercial confidentiality rules obscure how much profit private operators are making from prisons, and how much they are saving the various state governments across the Tasman.
Karen Batt of the Community and Public Sector Union, which represents 140,000 public sector employees, said the reports highlighted a lack of transparency and accountability and "serious questions" over the information provided by the companies.
Serco told RNZ that in Australia it had scored highly in independent reports in the last 12 months, from the Office of the Auditor General in Queensland, and the Western Australian Inspector of Custodial Services.
Serco said Acacia - the largest jail in Australia - is Western Australia's most efficient, costing $143 per prisoner per day, 40 percent less than other prisons in the state.
But Western Australian Prison Officers Union Secretary John Welch said it only achieved this by having dangerously low staffing levels.
"I think that the tide is turning, I think that people are starting to see that simply driving down costs is not a good way to run a prison.
"The big claim of the private sector is that they can do it more cheaply but ... a whole range of research out there says it is far from clear there is any saving whatsoever."
The West Australia Office of the Inspector of Custodial Services in its key findings from its 2016 check on Acacia said its day-to-day management was good.
But the state government "simply does not know if Acacia provides good value for money, because the total costs of running the prison is unknown", said the Inspector.
"The contract cost is publicly available; however, the [Corrections] Department has repeatedly failed to provide a robust estimate of additional overhead costs associated with the contract.
"Such a serious lack of financial accountability is not acceptable from any government agency, least of all one that expects to spend over $900 million in the 2015/16 financial year."
The United States government announced in August it was ending its use of private incarceration entirely at federal level. In a memo to officials, US Deputy Attorney General Sally Yates said they "do not save substantially on costs" and "do not maintain the same level of safety and security."