Southgate's former Three Lions team-mate and fellow defender Sol Campbell has claimed in a new authorised biography serialised in the Sunday Times that he would have ''been England captain for more than 10 years'' had he been white.
Campbell - who skippered his country three times, all in friendlies, and won 73 caps in total - also suggested the Football Association and "probably the majority of fans" do not want a black England captain.
Giving his reaction to the comments, England Under-21s boss Southgate said: "First and foremost, it is difficult to for me to know exactly how Sol feels because I have not walked in his shoes.
"In terms of the captaincy, I would be amazed if any manager picked somebody for any reason other than that he was considered to be the best leader for the team at that time.
"I have to say that I don't ever remember speaking to any manager who had been put under pressure to pick somebody as the captain who they didn't think should be.
"I think when we are critical of an organisation, it is a little unfair because that covers a lot of people.
"We have 850 employees here, so if we are critical of the FA, that is a broad statement.
"I think you always have to be careful when you go down that route."
Southgate added: "I think one of the things we are conscious of is promoting more black players becoming qualified coaches and more black people generally becoming qualified coaches.
"I think it is fair to say that the balance at the moment is not representative given the number of players.
"Guys are starting to come through, and we have to make sure that keeps happening."