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."

The grant will see the Penleaze Wing at Highcliffe Castle, near Christchurch restored and reopened to the public.
The work is one of the final stages to repair the whole of the Grade I listed building.
The house, owned and run by Christchurch Borough Council was mostly destroyed by a fire in the 1950s.
Nerys Watts, from the Heritage Lottery Fund, said: "These exciting plans mean that the last piece in the conservation jigsaw can be put in place at Lord Stuart de Rothesay's fantasy house."
Once the work is completed, it is hoped the original furniture, currently held at the Victoria and Albert Museum, will be loaned back.
The exterior of the building was restored following a Heritage Lottery Fund grant in 1995.
The castle was built in the 1830s by Lord Stuart de Rothesay and was once home to retail magnate Harry Gordon Selfridge, who lived at the castle between 1916 and 1922.
A four-month-old baby's murder by her father could not have been predicted, a serious case review has found.
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Plans to repair a derelict wing at a cliff-top mansion in Dorset have been boosted by £2,829,700 of Heritage Lottery Funding.