A serious case review found that Jonty Bravery, who is autistic, had expressed a desire to hurt people prior to the attack on the six-year-old in 2019.
He also had a personality disorder that had not been diagnosed and this was the explanation for the offence, it found.
The review calls for “critical lessons” to be “translated into action”.
Professionals failed to distinguish between behaviours linked to his autism and callous, premeditated traits, the report says.
It highlights a series of troubling incidents involving Bravery in the two years before the attack, including threatening to kill members of the public and putting faeces in his mother’s make-up brushes.
But his violent behaviour had been less frequent in the period before the Tate Modern attack, while he was living in a placement.
The report says: “There was no recent evidence that he presented a risk to other children or adults unknown to him.
“It was in this context that he was progressively given more freedoms, which saw him able to visit central London unaccompanied on the day of the incident.”
The review, by the Local Safeguarding Children Partnership (LSCP), highlights a national shortage of specialist and residential community care for children and young people with complex and high-risk behaviours.
A psychiatric report in 2018 said Bravery, who is now 19, had learnt to use his autism as an excuse to evade responsibility for dangerous behaviour.
The review says Bravery needed residential therapeutic solutions that could enable him, as an autistic young person, to engage in a treatment regime for his conduct disorder.
“But such a residential option did not exist,” it adds.
The LCSP says it is continuing to make improvements across police, health and social care in the delivery and co-ordination of support for autistic children and those with complex high-risk behaviours.