"There are certain things that possibly Lee-Anne needs to be compensated for,'' he said.
"But I think those discussions are better had over a period of time with the realities of what things actually cost rather than this type of environment.''
Ms Cartier told APNZ after the trial last year that she wanted compensation.
:"Financially it's crushed me. It's something that I haven't been able to let go. I need my money back for all the money I spent trying to do the cops' job.''
She said she spent thousands of dollars on phone calls and flights to Christchurch to further her inquiries.
"Phil's murder took over my life. I'd constantly be thinking about it. Before [Milner] was arrested I'd be up in the middle of the night putting two and two together. I guess it became obsessive, but I just wanted justice.''
Commenting after Milner's conviction, Mr Fitzgerald accepted the first investigation was badly flawed.
"It wasn't treated as a homicide. Unfortunately, that was the mistake that was made.''
An internal police investigation was carried out and the Independent Police Conduct Authority brought in.
The IPCA did not take things further but the first officers in charge of the investigation had been "counselled over their treatment'' of the initial inquiry, Mr Fitzgerald said.
"They were spoken to in respect of their shortcomings and everything was made clear as to what those shortcomings were.''
