Football Association chairman Greg Dyke responded to criticism of his commission to improve the England team by stressing he is still keen to recruit black and ethnic members.
Heather Rabbatts, the FA's only female board member, criticised the group's all-white, all-male make-up.
Dyke admitted making a "mistake" in announcing only part of the line-up.
But he added: "To suggest we never considered the ethnic balance of the commission is unfair."
Jamaica-born Rabbatts, 57, wrote a letter to Dyke and fellow board members to complain about "a lack of diversity", saying she had no choice but to go public as there had been a "refusal to understand" her position in private.
Rabbatts said: "The opportunity to lead an informed debate on the future of English players has been singularly damaged."
In an open letter in response, Dyke said he was "sorry" Rabbatts felt the need to go public and "surprised" at the comments of his former board colleague at the BBC, where he was director-general from 2000 to 2004.
Dyke wrote: "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."
The eight names announced for the commission are Dyke, FA vice-chairman Roger Burden, former England manager Glenn Hoddle, ex-England defender Danny Mills, League Managers' Association chairman Howard Wilkinson, Professional Footballers' Association chairman Ritchie Humphreys, Football League chairman Greg Clarke, and Crewe director of football Dario Gradi.
The group will consider how to increase the number of England-qualified players appearing for the country's top clubs. In September, Dyke set England targets of reaching the Euro 2020 semi-finals and winning the World Cup in 2022.
Dyke added in his letter that he had attempted to bring ethnic minority representation on to the FA commission by including Clarke Carlisle, the former chairman of the Professional Footballers' Association.
He wrote: "We originally had Clarke Carlisle as a member, but the PFA decided they would rather have their new chairman [Humphreys] on the commission. 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, 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."
The new sports minister Helen Grant, who is also equalities minister, says she will speak to the FA next week to express her concerns about the commission.
"Sports governing bodies must reflect the make-up of the diverse society that we live in," she said. "I expect the FA to ensure that voices from all backgrounds are heard loud and clear and contribute to this important piece of work to help strengthen English football. I will discuss the issue with the FA next week."
Piara Powar, executive director of European anti-racism body Fare and a member of Fifa's new anti-racism taskforce, said: "Heather Rabbatts is the first woman and only ethnic minority on the FA Board. She has ideas, experience and nous. But seems to have been ignored. Why?"
Lord Ouseley, chairman of anti-racism campaigning group Kick It Out, said he had raised the issue of the commission with Dyke, and questioned why he had not used Rabbatts' contacts and experience to bring on a suitable representative.
"This has been a disaster for the FA in public relations terms. Heather must have been at her wits' end to go public like this," he said.
"I find it very surprising therefore that someone as close to the chairman as Heather Rabbatts, with all her experience and contacts, was not asked for her advice on ensuring diversity."