Mr Balls, who was Children's Secretary at the time, said he had had to remove Sharon Shoesmith as Haringey Council's director of children's services in order to maintain public confidence in the child protection system.
The council's accounts show that Ms Shoesmith received a total of £679,452 in payouts following her dismissal from her £133,000-a-year role in December 2008 after a damning Ofsted report on the death of 17-month-old Peter Connelly.
Mr Balls said he was "frustrated" by the court's ruling, but said that he would make the same decision again.
"I had a duty to children in Haringey and across the country to act. It was my judgment that that was the only way to keep confidence in children's services," he said.
Mr Balls said the courts had ruled that Ms Shoesmith had been unfairly dismissed because he had not met her before removing her from her job. However he said he had been acting on the advice of government lawyers who told him it would have been improper to see her.
Baby P suffered more than 50 injuries despite being on the at-risk register and receiving 60 visits from social workers, police and health professionals over the final eight months of his life.