The proportion of inmates with prisoner management plans set up in appropriate timeframes was just 28 per cent, well below the target of 92 per cent.
Corrections deputy chief executive Christine Stevenson said Serco would be expected to improve significantly in its next quarter.
"It's quite a tough job and we set them some very high expectations. But they need to lift their game."
Mr Mahoney said it was always going to take time for Serco to adapt to managing a New Zealand prison and the targets were set "at very challenging levels" representing international best practice.
"The team there at Mt Eden are working very hard to improve," he told Radio NZ.
"We've invested in systems and people and I think we've learnt techniques to really deliver some positive outcomes."
Corrections Minister Anne Tolley said Serco was making "decent" progress in its first year.
"This is a very demanding contract ... As a private company they can be fined, or payments can be withheld, if there are any issues with performance."
The prison had been fined $400,000 in its first nine months because of a prisoner escape, three wrongful detentions, three wrongful releases and administrative errors.
The operator could be fined $150,000 for escaped prisoners and $25,000 for wrongful detentions, but also received financial incentives if assault and drug rates were low.
The prison had excelled in some areas under Serco's control. Positive drug tests had dropped, and there had been no incidents of self-harm.
Corrections said it was considering applying some of Serco's innovations to public prisons, such as making prison visits more "family-friendly" by allowing inmates more time with their children. This was believed to reduce criminals' likelihood of reoffending.
The target set by the departments for escapes, wrongful detentions, wrongful releases and loss of control (such as riots) was zero - the same targets as state-run prisons.
Asked whether Mt Eden was performing better than when it was Government-managed, Ms Stevenson said: "We run 19 prisons of which this is one. Each prison is a bit different. They've got a bit of work to do, I would say."
TRACK RECORD
* Mt Eden Correctional Facility
* Wrongful detentions: 3 (target: zero).
* Wrongful releases: 3 (target: zero).
* Prisoner escapes from custody: 1 (target: zero).
* percentage of positive drug tests: 2.82 per cent (target: less than 12 per cent).
* Rate of self-harm incidents: zero (target: zero).
* Rate of serious assaults: 1.07 per 100 prisoners a year (target: less than 0.9 a year).