Moyes has apologised for the exchange with BBC Newcastle and Radio Five Live reporter Vicki Sparks after the Black Cats’ 0-0 Premier League draw with Burnley at the Stadium of Light on March 18.
And speaking at a press conference on Monday, the Scot said: “It was in the heat of the moment. I deeply regret the comments I made.
“That’s certainly not the person I am. I’ve accepted the mistake. I spoke to the BBC reporter, who accepted my apology.”
The shadow Sports Minister has called on the Football Association to take action against Moyes, branding his comments “sexist threats”.
Sparks had asked if owner Ellis Short’s presence at the Burnley game had meant he was under more pressure with the club once again fighting a battle against relegation.
Footage published by the Daily Star shows Moyes answering, “No, none at all” before the interview drew to a close.
However, thinking he was off camera, he then added: “You were just getting a wee bit naughty at the end there, so just watch yourself. You still might get a slap even though you’re a woman.
“Careful the next time you come in.”
Both Moyes and Sparks were laughing during the exchange and the reporter did not make a complaint, although colleagues were unimpressed when they heard what had been said.
It is understood Moyes later apologised during a telephone conversation.
However, Dr Rosena Allin-Khan, the shadow Sports Minister, branded Moyes’ conduct “disgraceful”, adding on Twitter: “David Moyes cannot get away with these sexist threats - the @FA must take action immediately.”
Gary Lineker also condemned Moyes’ behaviour, saying on Twitter: “Moyes incident highlights a tendency for some managers to treat interviewers with utter disdain. Pressured job. Well rewarded. Inexcusable.”
A Sunderland spokesman said: “David and the reporter spoke to one another subsequently and the matter was resolved amicably.”
The BBC confirmed that Moyes and Sparks had spoken since and that the matter was resolved.
A spokesman said: “Mr Moyes has apologised to our reporter and she has accepted his apology.”
News of the incident emerged just days after Moyes confirmed he expects to remain in charge at the club next season no matter what happens.
Sunderland remain rooted to the foot of the table following Saturday’s 1-0 defeat at Watford and are eight points adrift of safety ahead of Tuesday night’s trip to Leicester.