Tomas Driukas, 26, from Birmingham, was jailed for life in 2016 for killing his daughter Deimante Driukaite.
An investigation found the baby died as a result of a brain trauma consistent with being shaken with force.
The NSPCC said the review highlighted that healthcare professionals "must leave no stone unturned when dealing with vulnerable families".
Police said Driukas had shaken his daughter because she would not stop crying.
Deimante died on 1 April 2015 in hospital after her father called an ambulance to the family home in Perry Barr, Birmingham.
The serious case review said Driukas and his partner were Lithuanians who had settled in England in 2010.
Its author Jim Stewart, an independent social work consultant, said the family had faced pressures related to Deimante being born prematurely and having complex health needs.
"They were young parents living in another country... clearly facing a challenge," he added.
"The family lived in a privately rented multiple-occupancy house and had limited extended family support."
Mr Stewart said the family's needs were not clearly understood by healthcare professionals.
"A significant opportunity was missed to explore the complex needs, [the] parents' capacity to meet their needs, cramped home conditions and for joint planning between hospital and community health professionals."
However, the report concluded Deimante's death could not have been prevented.
An NSPCC spokesperson said: "Deimante suffered horrifically at the hands of her own father, who carries sole responsibility for her violent and tragically early death.
"While Tomas Driukas's vile actions could not have been predicted, the review highlights that professionals in Birmingham and elsewhere must leave no stone unturned when dealing with vulnerable families with complex needs."
A four-month-old baby's murder by her father could not have been predicted, a serious case review has found.