They were also attacked following the handling of the Eniola Aluko controversy with ex-England women's coach, Mark Sampson.
In a bid to fix the damage left by the Eni Aluko discrimination storm, Wembley officials have responded with new initiatives created to make the FA "a more inclusive and diverse organisation".
FA chief executive Martin Glenn has suggested that women in sport will not "put up with" so-called "banter" in the same way as men as he announced a new grievance procedure at his organisation.
But Tuesday's briefing did not go entirely smoothly.
But the chief exec put his foot in it again when asked about the review of the culture around the England women's team.
It's named after Dan Rooney, former owner of the Pittsburgh Steelers and former chairman of the NFL's diversity committee.
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The sacking of Dungy and Green meant there were just two black and ethnic minorities (BAME) head coaches in the NFL. The team now requires a new coach.
The Eniola Aluko saga, which ended with former England women's boss Mark Sampson being found to have made racially inappropriate remarks, trashed the reputation of Glenn and the FA. Chris Hughton at Brighton is the only black manager in the 20-team Premier League.
"I think in talking to people at the Premier League and the FA, I don't see any resistance to it and to be fair the EFL has a Rooney rule in place".
'We are there to set an example, ' said Glenn.
"Now our grievance and whistle-blowing procedures are common across men's and women's teams".
"I think the Rooney Rule on its own isn't enough", said Glenn.
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There has never been a non-white manager of the England men's team, but the women's team was led into the 2007 and 2011 World Cups by Hope Powell, who is black. Glenn added that 13 per cent of the FA staff are BAME, which he said was above average for a United Kingdom employer.
The FA says this move will apply to jobs across England teams but BAME applicants will still need to show they meet the relevant recruitment criteria.
"The FA wants to become a more inclusive organisation where the workforce more represents the people who play football today", Glenn told BBC Sport.
"What it will say is the opportunity to have a career beyond playing is something that the FA is serious about promoting".
"It's all about improving performance by making the England players feel like the setup is more inclusive", Glenn said.
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