Dyke accepted he had "made a mistake" by only announcing some of the names on his commission at the Leaders In Football Conference earlier this month, with the eight on the list confirmed at that time being male and white, leading to Rabbatts' criticism.
Dyke wrote in a letter seen by Press Association Sport: "The make-up of the commission has been moving for some time but I did explain to you and the board that we planned to appoint two or three additional members and would have done so this week had the issue of Roy Hodgson's dressing room comments not blown up.
"I do accept we made a mistake announcing only part of the membership of the commission when we did, but to suggest we never considered the ethnic balance of the commission is unfair."
Dyke continued: "We originally had Clarke Carlisle as a member but the PFA decided they would rather have their new chairman (Ritchie Humphreys) on the commission, and we also identified other individuals from the BAME (black, Asian and minority ethnic) community who we felt would add strength and value to the commission.
"Unfortunately as they are active in football on a day-to-day basis either they felt the time commitments would be prohibitive. As you know we still want to see people with relevant experience from the BAME community on the commission and giving evidence to it."
Rabbatts, who was born in Jamaica and is of mixed race, has written to all fellow board members criticising the lack of diversity on the commission.
In her letter she says she has tried to raise the issue privately but there has been a "refusal to understand" her position.
The letter from Rabbatts states: "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.
"What is required is not tokenism but the involvement of individuals who have direct and relevant experience of what it means to represent their country while coming from diverse cultural backgrounds.
"By proceeding along this current path we are not only failing to reflect our national game but we are also letting down so many black and ethnic minority people - players, ex-players, coaches and volunteers, who have so much to offer and are so often discouraged and disheartened by the attitudes they encounter.
"The FA should be leading by example not reinforcing entrenched attitudes."
As well as Dyke and Humphreys, the commission also currently includes former England manager Glenn Hoddle, Football League chairman Greg Clarke and FA vice-chairman Roger Burden, League Managers' Association chairman Howard Wilkinson, Crewe director of football Dario Gradi and former England defender Danny Mills.
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