Sky Sports News has obtained a copy of a letter sent by Rabbatts to her fellow board members in which she criticised the lack of diversity on the new FA Commission set up to investigate the state of the game.
Rabbatts, who was born in Jamaica and is of mixed race, believes the organisation has "damaged" the chance to have an informed debate on the future of English players.
She suggested it was "ironic" there are no representatives from the black and ethnic minority communities - at a time when Andros Townsend helped England secure World Cup qualification.
Rabbatts insists she tried to raise these issues privately, but a refusal to understand her position left her with no option but to go public.
The letter read: "As you all know from my comments at the Board this week, I believe that the lack of proper consultation on the make up of the Commission, the fact that no approval was sought from the Board, releasing the names of the "chosen" individuals at Leaders in Football, the composition of the Commission itself and the lack of diversity, have all meant that the opportunity to lead an informed debate on the future of English players has been singularly damaged.
"I make the comments about diversity not because they are additional to this matter but because they lie at its heart.
"Indeed, while England's victories on Friday and Tuesday are due to many factors no one would argue that a young Black player made a huge difference and a young man whose father has played a significant role in fighting racism in football.
"It is therefore particularly ironic that a Commission to look at the national team has been formed with absolutely no representation from the Black and Ethnic Minority communities, many of whom play such an important role at every level of our game."
Rabbatts did defend England manager Roy Hodgson following his controversial dressing room joke about a monkey in space.
She wrote: "And during the storm over the manager I have totally supported the FA's position and Roy himself and knowing Roy as I do, I have huge respect for him and have no doubt he feels deep regret over the incident.
"However, on the issue of the Commission, I have come to the conclusion that the FA's current position is not sustainable and my own personal integrity and values are being compromised."
England boss Hodgson used a joke to illustrate the need for his team to give Townsend the ball in Tuesday's 2-0 win over Poland.
This incident has since been leaked to the press, sparking a row which led to a letter of complaint being sent to the Football Association by a pressure group.
Hodgson expressed frustration that his side's achievement in reaching the World Cup had been overshadowed and Townsend has echoed this view.
"It has all been said now, it has been in the news the last few days and I think everyone should focus on us qualifying for Brazil and not focusing on negative, silly news," he said.
"The manager told the player to give the ball to me, so that is a compliment in a way."