Campbell, who played 73 times for his country, claims in a new authorised biography serialised in the Sunday Times that the Football Association and the majority of fans do not want a black England skipper.
The 39-year-old said: "I believe if I was white, I would have been England captain for more than 10 years - it's as simple as that.
"I think the FA wished I was white. I had the credibility, performance-wise to be captain."
On the appointment of Michael Owen, who wore the armband on eight occasions, ahead of him, Campbell added: "I think the FA didn't want me to have a voice. Owen was a fantastic forward but nowhere near being a captain. It was embarrassing.
"I've asked myself many times why I wasn't. I keep coming up with the same answer. It was the colour of my skin."
The 39-year-old led his country three times in friendly matches, and Eriksson - who selected Campbell 32 times during his five-year reign - insisted in the Daily Telegraph that he had come under no pressure from the FA not to give the defender the armband on a more permanent basis.
"Not a chance - during my years, not a chance," the Swede said. "As you know, from my first to my last game, I had David Beckham (as captain) and there were never, ever any discussions at all in the team or in the FA about the captain."
Former England striker Ian Wright also disputed his ex-international team-mate's accusations, pointing out there were more suitable candidates around for the captaincy at the time.
"I think he's got the credentials to be captain, but to be captain for 10 years? I'm not sure when you see some of the players that were around then," said Wright, who played with Campbell for the Three Lions in the late 1990s.
Speaking on BBC Radio 5 Live's 606 show, Wright added: "I want a captain that goes in and gets you going. Sol has never had the demeanour where he is aggressive on the pitch and put people in their place.
"People say David Beckham wasn't like that, but he only had to raise his eyebrows to put someone in their place. Maybe Sol could have grown into it but it's down to the manager who he wants.
"Sol was more than good enough to be a captain but I personally believe there were better candidates at the time."
It is understood the FA is not planning to respond directly to the allegations.
Former FA executive director David Davies, who was at the organisation when Campbell was a player, said he was "surprised" by the allegations and believed they were "wrong".
"I am surprised by this because the reality is that in my time the managers selected the captain," Davies told BBC Radio 5 Live's Sportsweek programme.
"I never - and to my knowledge nobody else in the FA - ever sought to influence them.
"My belief is (the allegations) are wrong."