The broadcaster, 60, was taken off air after breaking restrictions for her birthday party in London in December, which was then in Tier 2.
Burley returned to Sky News on June 7.
She has now said she that she was “appropriately sanctioned” and apologised to viewers and friends for her actions.
Speaking to the Daily Mail, 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.”
The presenter had been part of a group that dined at two tables in one venue and then visited another before a group of four went back to her home.
Following an internal review in December, Sky News found “a small number of Sky News 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.”
The channel’s political editor, Beth Rigby, and correspondent Inzamam Rashid were also taken off air for three months following the review.