Former Professional Footballers Association (PFA) chairman Carlisle made the claim a day after Dyke accepted the FA "made a mistake" in only announcing part of the membership after board member Heather Rabbatts criticised the all-white line-up.
Rabbatts, who was born in Jamaica and is of mixed race, wrote to all her fellow board members criticising the commission's lack of diversity after saying her attempts to raise the matter privately failed to gain an acceptable response.
As well as Dyke and new PFA chairman Ritchie Humphreys, the commission also 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.
But now Humphreys' predecessor Carlisle claims it was "inevitable" that criticism would follow when the FA chose only to release the names of white male participants.
He told to BBC Radio 5 Live's Sportsweek programme: "My view of the FA is that a lot of their mechanisms have been terrible for many, many years. When Greg Dyke took the helm I was expecting, with all his experience at such a huge organisation like the BBC and the way that he oversaw change there, that he would be able to translate that into what they do at the FA.
"The biggest mistake I feel Greg Dyke made was announcing part of its constitution. If he was going to make sure there was representation on the commission, then surely he should have waited until he had the full line-up and then roll it out.
"Rolling out 80 per cent of what the commission is and people only seeing Caucasian male faces will inevitably lead to this discussion."
Chesterfield defender Humphreys replaced Carlisle as head of the players' union last month but his predecessor says he has no problem with the new chairman representing England's footballers on the commission.
"If I was asked, of course I would love to be involved if we could address the state of English football.
"But Ritchie is a fantastic man and he does represent the entirety of our membership."
Among the other names tipped to join Dyke's commission is Manchester United defender Rio Ferdinand.
Carlisle would welcome his involvement but insisted the membership should not be limited to those who have played in the Barclays Premier League.
On Ferdinand's involvement, he said: "It would make sense. First of all you have to look at the remit of the commission and I have really tried to find this because it has been ambiguous all the way throughout.
"The most conclusive statement that I can find is that [the commission is for] 'the future of English football'. Now if you are going to set up a commission for that, not only do you need to have a commission to represent the constituents of English football, but one that doesn't just represent the upper echelons of our system, because the problems are right throughout, from grassroots right to the senior England team.
"But the only people we have on the commission are people who have experienced football right at the elite end.
"Not only do we need diversity in hopefully a BME [black and mixed ethnicity] candidate to represent the cultural and racial differences, but what about gender? What the female game? What about schools football? What about the county FAs? What about someone like Colin Bridgeford at the Manchester County FA, who is overhauling their structure?"