Writer Neil Cross said Elba only accepted the role in the crime drama as race was not considered integral to the character.
Miranda Wayland, the BBC's head of creative diversity, told the MIPTV media conference: "When [Luther] first came out everybody loved the fact that Idris Elba was in there – a really strong, Black character lead.
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"We all fell in love with him. Who didn't, right? But after you got into about the second series you got kind of like, okay, he doesn't have any Black friends, he doesn't eat any Caribbean food, this doesn't feel authentic."
But Cross, who created the detective, said: "I have no knowledge or expertise or right to try to tackle in some way the experience of being a Black man in modern Britain.
'It would have been an act of tremendous arrogance for me to try to write a Black character. We would have ended up with a slightly embarrassed, ignorant, middle-class, White writer's idea of a Black character."
The BBC has said it is "tremendously proud" of Luther.
The corporation has pledged to spend £100m of its content budget on diverse programming over three years, following the Black Lives Matter movement last year.
The BBC is said to have made diversity part of "every conversation" about new shows and that the issue is "non-negotiable".
The crime drama starring Elba as DCI John Luther and Ruth Wilson as his adversary Alice Morgan launched in BBC One in 2010 and ran for five series until 2019.
Elba – who is an associate producer on the show – confirmed last year that a film spinoff is still in the works.
He said: "I’ve maintained I’d like to see it come to a film, and that is where I think we are heading towards – a film. And I’m looking forward to making that happen. It is happening.
“With film, the sky is the limit. You can be a little bit more bold with the storylines. And a little bit more international, and a little more up the scale. But John Luther is always going to be John Luther.”
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