He had removed her from her post as head of Haringey's children's services after Ofsted criticised the department's leadership.
Mr Balls had ordered its inspectors to look into Haringey's ability to protect children after a trial heard Baby P suffered injuries including a broken back and eight fractured ribs, despite 60 visits from professionals.
Haringey Council decided to fire Ms Shoesmith without pay shortly afterwards.
In her first interviews since her dismissal in December, Ms Shoesmith said she was "shocked" at how fast the death of the 17-month-old boy had become a party political issue.
"It just has been deeply reckless, breathtakingly reckless, and I don't think people really understood quite what the potential impact could be," she said.
"And now you've got this, a local tragedy and a national catastrophe."
Despite national difficulties in recruiting social workers, Mr Balls said: "I wasn't reckless. I didn't jump in, even though I was pressed to do so, I waited for an independent report.
"I sent in inspectors - the experts - to do the work. In a devastating report, they said there were real failures in management in Haringey.
"In the end the director of children's services has to take responsibility," he said, adding that he would do the same again if it was in the interests of children's safety.
The BBC's James Westhead said: "It's true that there's a recruitment crisis in social work. It's equally hard to say whether things would be any better if Sharon Shoesmith was still in charge."
Speaking to BBC Radio 4's Weekend Woman's Hour and the Guardian, Ms Shoesmith claimed she had been the victim of a press "witch-hunt".
She said she "grapples" with carrying personal responsibility for Baby P's death every day and had even considered suicide.
"Of course I've been distressed about this, of course I have, and had many sleepless nights over it," she said.
"Without being dramatic, I think when people are in the eye of the storm, as I was, you do consider how you might end it all and, of course, I did that.
"But if there's a young person killed through knife crime this weekend, and I hope there isn't, do we expect the borough commander of that London borough to resign? We don't, we don't."
The inspectors' report into her department criticised everything from insufficient supervision by senior management to poor record-keeping and a failure to identify children at immediate risk of harm.
Ed Balls tells the BBC "I did the right thing"
But Ms Shoesmith, who lost an appeal last month against her dismissal, defended her decision not to resign
She said there had been as many people asking her to "be strong" and resist resignation as had been calling for her to go and that her staff had needed her at the time.
Ofsted's inspectors gave her no opportunity to discuss their findings and that the good practices drawn to their attention were omitted from their report, she claimed.
"The first time I saw that report was when it was already published on a website accessible to the public," she said.
Baby P's mother admitted in court causing or allowing the boy's death and her boyfriend and lodger, Jason Owen, 36, were convicted of the same offence and await sentence.
At the time, Ms Shoesmith said "we can't stop people who are determined to kill children" and she used the interviews to defend this assertion, saying it was an "honest answer" that people did not want to hear.
She also defended her former department by saying that social and health workers had never seen a badly injured child. While there were concerns about Baby P, they did not meet the threshold for care proceedings, she added.
Labour MP Barry Sheerman, who chairs the Commons Education Committee, said he felt Ms Shoesmith had been treated "unfairly".
But he said that amid the media furore, intensified by Tory leader David Cameron using all his Prime Minister's Questions on one day to raise the case, Mr Balls had to "act decisively".
"In the wake of that, I do think that Sharon Shoesmith was treated unfairly but I don't think it helps anybody to have this kind of public recrimination," he said.
"What we need is to see that she is actually treated fairly, to reflect on the case and to make sure that social workers, who do such a good job up and down this country, are reassured that we know they do a good job and we value them."
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