In a 45-minute interview, the former au pair said she shook Matthew Eappen after she found him unconscious, in an effort to revive him.
CBS News Correspondent Vicki Mabrey reports that Woodward said she wasn't always as gentle as she could have been with the baby. But she denied causing his death.
Woodward told the BBC that the 8-month-old was "always toppling over," and could have hit his head the day before he was hospitalized.
Prosecutors claimed that Woodward fatally shook the baby. A Massachusetts jury convicted her of second-degree murder, but a judge reduced it to manslaughter and sentenced her to the 279 days she had already spent behind bars.
The baby's uncle says Woodward had her say in court. He says people shouldn't pay attention to her now.
Asked about the baby's parents, Woodward gave a short, nervous laugh and said, "I have no love for them. There's nothing I can tell them that they don't already know. They really tried to send me to prison."
She claimed in the interview she was really upset and really concerned because, when the baby's parents went to the hospital as soon as he was taken there, they were allowed to act as doctors on the case. She thought that was very strange.
Woodward said during the interview that she was not paid, and the BBC took great pains to let everyone know she - and her parents - did not receive payment for the interview and for the excerpts other media were allowed to use.
Both Woodward and her parents have repeatedly denied that they sold or had any intention of selling the story of Woodward's ordeal in the United States.
But a British newspaper on Saturday admitted paying 40,000 pounds ($66,800) to her parents last November and is now serializing her story.
The paper says they paid the money into Woodward's defense fund and that it was paid before she was convicted.
The BBC interview was conducted by Martin Bashir - the man to whom Princess Diana bared her soul in a sensational television interview in 1995, admitting she had committed adultery.
The choice of Bashir has infuriated sections of the media, which have already cooled towards Woodward only seven months after presenting her as an innocent British victim of an unfair U.S. justice system.
The Mirror on Monday blasted Woodward for modeling herself on Diana in her choice of a dark suit, similar to the one worn by the late princess for the interview with Bashir.
Opposition Conservative Member of Parliament Teddy Taylor said: "If Louise Woodward is trying to look like the princess, it's an insult. She should have more common sense."