Deputy Coroner Anthony Schapel found that the deaths of Korey Lee Mitchell, 5, and his six-year-old sister Amber Rose Rigney could and should have been prevented.
He criticised a lack of action from child-protection officials in the face of multiple reports of abuse and neglect.
Mr Schapel called for a comprehensive review to ensure child protection authorities were meeting all their statutory obligations and said a lack of resources should not be tolerated.
In the government's response on Friday, Child Protection Minister Katrine Hildyard said the report was "harrowing" and conceded there had been failings in child protection by successive administrations.
"I can't fix the past but I can work every single day towards making South Australia a place where vulnerable children are safer," she said.
"It breaks my heart that there are families grieving children because of those failings."
The minister said the government had accepted and would implement all the deputy coroner's recommendations and would move quickly to appoint an independent person to conduct the required review.
"We will also ensure that adequate resourcing is available for staff to fulfil their statutory obligations," she said.
"My approach as minister is to thoroughly examine systems and processes to make sure we are doing everything that we can to prevent tragedies from occurring, to intervene wherever possible and to make sure we give the most vulnerable South Australian children the best opportunity to mentally, emotionally and physically thrive."
In his findings, Mr Schapel said a proper investigation would have revealed the completely unsatisfactory nature of how Korey and Amber were being cared for.
"This family required extremely close scrutiny and supervision," he said.
"The mother's amphetamine usage should have been the subject of an examination and have been curtailed.
"To my mind, the police should have been asked to investigate these allegations."
Steven Graham Peet is serving a 36-year non-parole period after pleading guilty to killing both children and their mother, Adeline Yvette Wilson-Rigney, in May 2016.
He was not the father of the children but was living with them and their mother at the time.
Mr Schapel said that for a significant period leading up to their murders, the children lived in an environment that was on any objective analysis dysfunctional.
"Needless to say, responsibility for these callous murders lies with Peet," he said.
"This inquest was undertaken to ascertain whether or not the deaths could have been prevented by the child protection authorities assuming a more vigorous role in relation to the protection of the two children.
"The answer to this question is that their deaths could and should have been prevented."
