The presenter was taken off air at the end of last year after breaking Covid-19 rules with a birthday gathering.
Speaking to the Daily Mail, Burley has now said she was “appropriately sanctioned”.
She said: “I thought I was Covid-compliant. I wasn’t. I made a mistake.
“I was an idiot and I let myself and my viewers down. I’m sorry for what I did and for any heartache I caused the loyal friends with me at the time.
“I was appropriately sanctioned.”
She added: “I paid for my mistake; quite rightly. My viewers told me how frustrated they were with me and they were right to do so.
“With time, the mood music changed and my viewers wanted me back.”
Burley had celebrated her birthday with a rule-breaking gathering in London in December, while the capital was under Tier 2 restrictions.
The presenter, who has been with Sky News since its inception in 1989, apologised at the time, tweeting: “It doesn’t matter that I thought I was Covid-compliant on a recent social event. The fact is I was wrong, I made a big mistake, and I am sorry.”
Following an internal review in December, Sky News found that “a small number of staff attended a social event in London” where Covid-19 guidelines were breached.
It said: “All those involved regret the incident and have apologised. Everyone at Sky News is expected to comply with the rules and the company takes breaches like this very seriously indeed.”
Burley returned to her breakfast slot on Sky News earlier this month.