On Saturday, Rabbatts criticised the panel being all-white and all-male - the FA have since appointed Roy Hodgson and Rio Ferdinand to the commission that will look how to improve the England team.
Rabbatts has welcomed their inclusion but believes the real issue of diversity is still not fully resolved.
"While I can appreciate the appointment of Roy and Rio and of course welcome a degree of diversity, there are still questions which remain about the work and role of the FA Commission," said FA board member Rabbatts.
"Like many who have spoken out I want to see the Commission be successful in its mission to strengthen the future talent pool for the England team.
"However, the issue of real diversity, and the insight that can bring, is still not fully resolved nor are the exact terms of reference of the Commission and the continued absence of the Premier League from its membership."
Helen Grant, who holds the dual portfolio of sports minister and equalities minister, also admitted she was concerned by the original selections.
FA chairman Greg Dyke will head up the body, while 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 already confirmed.
"It is important Roy can offer his views as the current manager of the national team and share the knowledge he has gained when working for many years in a number of countries," Dyke said in an official FA statement.
"I wanted the international fixtures to be completed before announcing this to avoid any distractions for Roy at such an important time.
"Rio's vast experience as a player developed through West Ham's successful youth system, winning Premier League and European titles with Manchester United and representing England at World Cups means he has a huge amount to offer to the debate.
"We have been speaking to Rio and Manchester United for some time about him joining the group - before we named the other members of the Commission.
Former England manager Hoddle welcomed the announcement that Hodgson and Ferdinand would also be consulted.
He said: "I think people like this (being involved), it's going to be invaluable.
"Rio is a very astute guy to be putting on there with his experience. He is still playing and has a lot of respect in the game. It will be lovely to hear his perspective."