FA must investigate David Moyes comments, says Wearside domestic abuse charity
Moyes said he "deeply regrets" the exchange with BBC Radio Five Live reporter Vicki Sparks following his side's 0-0 Premier League draw at home against Burnley on March 18.
Sparks had asked if owner Ellis Short's presence at the game had meant he was under more pressure, with the club once again fighting relegation.
Footage published by the Daily Star shows the Scot 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 off-hand exchange and the reporter did not make a complaint.
Clare Phillipson, director of the domestic abuse charity Wearside Women in Need, was "stunned" when she watched the exchange on video.
She said: "I think the FA have to look into it.
"It is for the FA to set a clear standard about what they think is acceptable.
"It was dreadful, absolutely appalling.
"This is a woman, in a very small minority of sports journalists, trying to go about her job and being threatened.
"It's the sort of thing you expect down the local pub, not the kind of thing you get from a professional football manager."
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."
Ms Phillipson was critical of the club last season for continuing to pick Adam Johnson despite him being accused - and subsequently convicted - of sexual activity with a besotted 15-year-old fan.