Livingstone had twice breached a protection order preventing him from contacting Ms Webb in the months before the deaths.
During questioning today from Anne Stevens, counsel for Ms Webb, Southern district commander Superintendent Coster admitted police made a number of "significant failures" in their duty of care to Ms Webb and her children.
Despite that, he would not "speculate" as to whether police could have prevented the deaths.
"You are asking me to speculate what would have occurred if A, B, C, D had happened, I simply can't do that," he said.
"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 if police failure to follow up those matters might have contributed to the deaths.
"Katharine and the children not being home that night could have affected the final outcome.
"I'm not prepared to speculate on what might have happened."
Despite their failures police were "well intentioned" in their care of Ms Webb.
"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.
Earlier he said Livingstone thought about killing his children for some time.
"He had a sick ideation and [it] suggested a level of commitment to carry out these acts," he said.
The court heard from a former probation officer this morning.
Liqueshia Dougherty told the court the Livingstone family was discussed at a meeting of Dunedin's Family Violence Inter-Agency Response System agencies in August 2013.
At that meeting Livingstone was deemed a "high risk" to his family, but it appeared no further action was taken in regards to this information.
Livingstone shot Bradley and Ellen with a 12-gauge Stoeger shotgun.
He was found dead in the bedroom he formerly shared with his estranged wife, Ms Webb; a shotgun was found next to his body.
Livingstone stole the Stoeger shotgun used in the shooting from his one-time flatmate Philip Mans.
Livingstone stole the gun from Mr Mans' firearms cabinet using a key to Mr Mans' Milton house which was stolen at an earlier date, the court heard earlier this week.
Dr David Chaplow told the coroner's inquest it appeared Livingstone was weighing up his options in the days leading up to the killings.
Livingstone spoke to his new partner, Karen Wright, while drinking on a park bench little more than an hour before he shot his children with a 12-gauge shotgun, Dr Chaplow said.
"What we know from the lady friend [Ms Wright] is by half past 8[pm on January 15, 2014] he was sitting in a park feeling quite morose and thinking about what he's going to do," he said.
It appeared Livingstone was "hedging his bets" for some time before the killings.
"It seemed to me he had been thinking about his options, so to speak, for a day or two - hence stealing the gun, stealing the key," Dr Chaplow said.
Despite a number of "red flags" coming to the attention of the clinicians dealing with Livingstone, the slayings were ultimately unavoidable, Dr Chaplow said yesterday.
Robin Bates QC, counsel for police, asked "if somebody makes up their mind to do this sort of thing, there's a high likelihood they will do this despite all the interventions, is that a correct comment?".
"That is a correct comment," Dr Chaplow said.
Livingstone seemed to "impression manage" his clinicians, not allowing them to gain a full insight to his personality.
Livingstone's duplicity became apparent during day one of the inquest when the court heard he had deceived his psychiatrist Dr Christopher Wisely.
A co-worker told the court on Tuesday she felt Livingstone knew "what to say to the right people to get them off his back".
Livingstone often smelt of alcohol at work and appeared dishevelled in the months leading up to breaching his protection order twice.
Livingstone was convicted of arson and assault in Australia in 1988.
Ms Webb sought a protection order and it was first issued on May 31, 2013, and finalised on August 13.
On August 7, 2013, Livingstone breached the order for the first time.
The inquest has concluded and Judge Marshall reserved her findings.
