Leicestershire Police and two councils were criticised at yesterday's inquest ruling into the deaths of Fiona Pilkington and her 18-year-old daughter, Francecca Hardwick.
The verdict came ahead of a new crackdown on problem families who terrorise their neighbours to be unveiled by the Prime Minister today.
Gordon Brown will promise to stand by "the lawful majority" against families who let their children run around out of control.
Ms Pilkington, 38, killed herself and her daughter, who had a mental age of four, by setting light to her Austin Maestro while they both sat inside at a lay-by near her home in Barwell, Leicestershire.
Together with the single mother's severely dyslexic son Anthony, they suffered more than 10 years of abuse from a gang of teenagers living in their street.
Inquest jurors found the police's failure to respond to dozens of the family's pleas for help contributed to the deaths in October 2007.
They also criticised a failure by police and Hinckley and Bosworth Borough Council to share information, which they said was one of the main reasons so little was done, and Leicestershire County Council for failing to properly help the family.
Home Secretary Alan Johnson said police and councils had "some hard lessons" to learn, while shadow home secretary Chris Grayling said the law seemed to allow troublemakers to "get away with it".
In a press conference at Loughborough Town Hall after yesterday's inquest verdict, Temporary Chief Constable of Leicestershire Constabulary Chris Eyre offered his "unreserved apologies" to Ms Pilkington's family.
He said: "We are extremely sorry that at times our actions failed to meet the family's needs and in retrospect there are things we would have done differently.
"I would like to offer my unreserved apologies to the family, community and wider public."
Mr Eyre said the force launched an investigation after reading a suicide note from the full-time carer in which she talked about the family's ordeal and questioned the police's response.
He admitted the vulnerability of Ms Pilkington's family had not been picked up, but said improvements had been made since their deaths.
Mr Eyre said no individual officers had been disciplined. But the Independent Police Complaints Commission (IPCC) is now investigating.
He added the force would take action against any residents on Bardon Road continuing to cause problems.
Mr Eyre said: "Many incidents of anti social behaviour are extremely difficult to deal with.
"There's no panacea and we have to work very hard to make sure that where incidents of anti-social behaviour are occurring they are dealt with in the right way."
The inquest heard 33 calls were made to police about Ms Pilkington suffering anti-social behaviour in 10 years.
Her family's ordeal included stones, eggs and flour being thrown at their home, while on one occasion the 16-strong mob shouted at Francecca to lift up her nightdress.
Anthony, 19, was also marched to a shed at knifepoint and locked in by the gang - some as young as 10.
Ms Pilkington was given an anti-social behaviour log by council officials so she could document the abuse and reveal how she felt about it. But the harrowing diary was only discovered after she killed herself and her daughter.
Hinckley and Bosworth Borough Council sought an injunction against neighbours Steven Simmons, 43, and his 44-year-old wife Susanne, who have four children.
It has since expired as neither the council nor police brought any further evidence against them in the year it was in place.
Home Secretary Mr Johnson said: "This has been a shocking and immensely distressing case. For more than a decade, the Pilkington family suffered intimidation at the hands of a local gang, culminating in a sustained level of abuse that no family should have to tolerate."
Coroner Olivia Davison told the inquest she plans to write a report to the head of the borough council, which would be copied to the Ministry of Justice.
She said: "I am concerned about the evidence I have received in this inquest about the process for gathering and recording information from victims of anti-social abuse."
Speaking after the inquest Pam and David Cassell, Ms Pilkington's parents, said the case highlighted difficulties faced by families with disabled children.
They said: "If this helps just one family then their deaths would not have been in vain and something good will have come out of this tragedy."
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