The four-day inquest concluded yesterday and Judge Marshall reserved her findings.
Mr Coster said he would not "speculate" as to whether police could have prevented the deaths if the mistakes were not made.
"All I can do is comment on what didn't occur."
Dunedin police failed to record and investigate a number of bullet cartridges that were given to the children by Livingstone, ostensibly as a present.
They also failed to appropriately follow up on Ms Webb's disclosure that Livingstone had trapped her in her room and raped her for five hours, at times while her distraught daughter banged on the bedroom door.
Police also granted Livingstone diversion for breaching the protection order, against national policing policy.
"Anything could have affected the final outcome," Mr Coster conceded when asked by Anne Stevens, counsel for Ms Webb, if police failure to follow up those matters might have contributed to the deaths.
Despite their failures police were "well intentioned" in their handling of the Livingstone matter.
"Police are 100 per cent committed to protecting victims and this is a really tragic case, but we can't change what happened," Mr Coster said, choking back tears.
Livingstone told several people about thoughts he had of killing his children.
However, those scenarios did not involve shooting the children, Mr Coster said. "The ideation he suggested was using an axe."
Ms Webb sought a protection order which was first issued on May 31, 2013, and finalised on August 13.