Dyke's first crisis since he took over the role came after FA board member Heather Rabbatts publicly criticised the all-white and all-male make-up of the commission.
Rabbatts was backed up by anti-discrimination groups, with sports and equalities minister Helen Grant also expressing concern. The FA has since announced Manchester United defender Rio Ferdinand, who is mixed race, and England manager Roy Hodgson will be part of the commission.
Dyke said: "I got rather annoyed by some suggestions. The idea I'm in any way disadvantaging people from different ethnic backgrounds is not true.
"We were talking to Rio at that time, we always wanted to get him on board.
"The commission will meet and it may be decided that we're missing some skills. We talked to a lot of people before we set it up but they're not all the same and the solutions aren't all the same."
Dyke, speaking on BBC's Football Focus, remains keen to increase the number of players available to the national team playing regularly at the highest level of English football or abroad.
He said: "We'll look at what's realistically possible and what can we achieve that can give English kids a chance of playing at the top level.
"We'll do a lot of research (and look at) what's happened in other countries - Spain, Germany and Belgium are all quite interesting.
"Where are the barriers to stop kids getting through the system? Some will say they aren't good enough but a lot of coaches will say there are barriers, so how do you get them into first teams?"