The 61-year-old – who became the FA's first female non-executive director in 2012 – said it had been a privilege to be the "first woman of colour" to be on the FA board and conceded that some progress had been made.
However, Rabbatts, whose place as chair of the FA Inclusion Advisory Board will be taken by former Chelsea defender Paul Elliott, said in a letter addressed to FA Chairman Greg Clarke that there was a danger of losing out on another generation of non-white coaches.
"There are of course significant challenges still to be addressed," wrote the Jamaican-born lawyer and businesswoman.
"Like you, I remain frustrated at the lack of progress for BAME (Black, Asian and minority ethnic) coaches and managers in the professional game.
"This is an issue not just for the clubs and leagues, but also for The FA within its England set up at St. George's Park.
"The Football League and Premier League are pursuing their initiatives and I would urge you and Paul to use your leadership to both work with them and to set the right example as the national federation for others to follow."
Brighton's Chris Hughton will be the only manager of colour in the Premier League next season and was another, in January, to express concerns over the lack of diversity among his colleagues.
"Currently we are in danger of losing, yet again, another generation of ex-players and other BAME individuals who want to play a role and have relevant skills and experience yet increasingly feel excluded," added Rabbatts.
"I know that there are really good intentions and a desire to make change but tangible action is required."
Clarke, who has overseen reforms to the make-up of the FA Board reducing it from 12 to 10 and increasing female representation to three, paid Rabbatts a handsome tribute.
"Her impact has been significant, most recently her support in getting the new FA Governance reforms ratified," said Clarke.
"As a result English football will be more inclusive and diverse than ever before."