The England boss and Manchester United defender were added to the already eight-strong team on Sunday but the decision was met with some derision from Rabbatts who feels that perhaps Dyke could have appointed someone from an ethnic minority.
"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," Rabbatts said.
"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."
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