Paul Wilson, 21, was jailed in 2011 after raping the little girl at a nursery in Nechells and videotaping the incident on his phone.
He has since been sentenced to a minimum of 13 1/2 years in prison.
The city's Safeguarding Children Board conducted the review, the BBC said.
The board found that Ofsted, the government agency responsible for inspecting schools and other facilities, was aware of the relationship, but failed to stop it, the BBC reported.
The review also stated a lack of supervision, the layout of the nursery and the weak safeguarding practice also led to the incident.
The board made eight recommendations based on its findings, and representatives from the agency said that blame should still rest with Wilson.
"Responsibility for this awful abuse must, and does, lie with the perpetrator," said Jane Held, who heads the board.