Sunderland manager Moyes has until Monday to provide the FA with his observations on a leaked exchange with the BBC interviewer Vicki Sparks, during which he suggested she "might get a slap even though you're a woman" and warned "careful next time you come in".
The Scot has apologised and the club have deemed the comments "wholly unacceptable" but further details have been requested by the governing body before any potential disciplinary action.
Rabbatts thinks the root issue reaches beyond just Moyes or one isolated incident, and exposes a concern.
"What I find surprising, whether it's comments made by Mr Moyes or indeed others, is we still see these comments and behaviours," she told BBC Radio Five Live's Sportsweek programme.
"I sit on other boards in other sectors, you just don't this anywhere else
There's a view that football is an exception because of the passion on the game, the heat.
"There are many other sports that have very passionate moments but we don't find that we experience these moments.
"(Regardless of) the heat of the moment or being passionate about a sport, there are standards of behaviour we hold dear, that go to the heart of respect
There isn't a moment where the heat releases you from those broader responsibilities of behaving ethically.
"It's fundamentally important that the values we all say we abide by in football are upheld, particularly by people who have huge power and are role models, whether they be managers, players or any of us involved at management level."
Rabbatts was keen not to rake over the specifics of the Moyes incident or pre-empt either Sunderland's submission to the FA or any subsequent judgement of it.
She did, though, suggest Moyes' job should not be on the line - at least for disciplinary reasons.
"He has apologised and there is a recognition that what happened was not appropriate," she said.
"Whether it is subject to any regulatory oversight is a different question, I think the issue of his tenure in his role will be more linked to results on the pitch."
Source : PA
Source: PA