Four-month-old Aalihya Jordan-Fellows suffered a fractured skull and died after being thrown into her cot by her uncle, Jason Roberts, at her home in Kings Heath, Birmingham, in December 2008.
Roberts, 25, was jailed for manslaughter last year but cleared of murder after a jury heard he had been "stressed and frustrated" because the baby would not stop crying.
He had been left alone to look after Aalihya by her mother, Bobiellen Jordan, 22.
She was given a community order after admitting a charge of child cruelty.
But a serious case review into the tragedy published yesterday concluded that the girl's death could have been prevented had the authorities acted differently.
It criticises Birmingham Social Services for failing to put safeguards in place when Aalihya was born despite knowing about the troubled past of her parents, who were both in their late teens and had grown up in care.
They knew about allegations of drug and alcohol misuse and police had specifically raised concerns about possible domestic abuse, the report discloses.
But an assessment decided that she was not in enough danger to be taken into care at birth and she later appeared to be meeting her developmental "milestones".
Crucially, the report discloses that Aalihya's father, Dean Fellows - who moved out after splitting up with Jordan - had specifically raised the alarm that Roberts, who was staying at the house, was being left alone with his daughter.
He told police that Roberts, his half-brother, had been arrested over allegations of "offences against a child" when he was a teenager, although never charged.
The report says that although police warned Jordan never to leave Aalihya with Roberts they were powerless to take the baby to safety because she had not been designated as at risk by social services.
The report finds: "Had the baby been subject to the above processes then the actions of the police on the evening in December 2008 would have been very different.
"If the baby was known to be subject to a child protection plan when found in the care of uncle, a known risk to children, then it is likely the baby would have
been removed using their emergency powers and would not have been in the
family home on the night the fatal injuries were sustained."
It finds that she had not been placed under the plan because the initial assessment process was flawed.
"The assessment failed to take account of the parents' troubled history, key information about their parenting capacity and the accumulated knowledge of the family held by partner agencies."
A spokesman for Birmingham City Council said: "We want to apologise unreservedly that the services that we gave Aaliyah in 2008 were not adequate to protect her.
"Significant changes have been made to children's social care in the last four years since her tragic death."