Ex-Arsenal and Tottenham Hotspur defender Campbell, who was born in east London to Jamaican parents, amassed 73 caps from 1996 to 2007 and captained England three times.
Graham Taylor, in charge of the national team between 1990 and 1993, was staggered by the accusations.
"Sol is making a real go of giving his book a good sell. I cannot go along with what he is saying," Taylor told BBC radio.
"I never had any influence on me to select who should be captain regardless of the colour of his skin."
The 39-year-old Campbell's claims were revealed in extracts from his biography being serialised in the Sunday Times newspaper.
"I don't think it will change because they don't want it to and probably the majority of fans don't want it either," Campbell said.
"It's alright to have black captains and mixed race in the Under-18s and Under-21s but not for the full national side. I think the FA wished I was white.
"I had the credibility, performance-wise, to be captain ... and I was a club captain early on in my career (at Tottenham). I believe if I was white I would've been England captain for over 10 years."
Taylor highlighted midfielder Paul Ince as England's first black skipper.
"No one from the Football Association ever gave me an impression that I shouldn't have given the captaincy to him. There was none of that in my managerial career," said the former Aston Villa and Watford manager.
Sven-Goran Eriksson, who gave Campbell the armband against the United States in 2005, told the Daily Telegraph newspaper there was "not a chance" the allegations were true.
Campbell said it was "embarrassing" that striker Michael Owen was made captain ahead of him by Eriksson but John Barnes, a trailblazer for black England players, believes the other skippers deserved the honour.
"I don't think Sol would have been captain for 10 years because if you look at the captains - they were Tony Adams and then after that Alan Shearer," Barnes said.
"Then David Beckham became captain and that was a PR exercise for the FA. I don't think necessarily it was because of the colour of Sol's skin."
Mark Palios, the FA's former chief executive, was "flabbergasted" by Campbell's comments.
"To brand the FA like that is just an example of lazy labelling and he does the case of fighting against racism no favours by saying this," he told BBC Radio 5 live.
"If you talk about the selection of the captain and the players, it was entirely down to the England manager.
"We would never go anywhere near suggesting to the manager who should be in his squad or who should be his captain," added Palios, who was FA chief executive in 2003-04.
"Sol has picked the wrong argument. If he had said something about the lack of opportunities for (black) coaches then everyone would have resonated with that."
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- Graham Taylor