In his first public comments on the issue, Beckham said he was disappointed Capello had quit the job so close to the European Championships, but said he respected his decision and believed the manager should always be allowed to choose the captain.
"I've been working with Fabio for quite a few years. It's sad, obviously that he stepped at a critical stage for England," Beckham told reporters after training with the LA Galaxy on Thursday.
"You know he's done it for his own reasons. You know he's a manager that I respect a lot, a person I respect a lot. I wish him all the best."
Capello's turbulent reign as England manager ended last week when he resigned after meeting with the FA, who stripped John Terry of the captaincy for allegedly racially abusing Queens Park Rangers' defender Anton Ferdinand.
Terry, who would have led England at this year's European Championships, denies the charge and Capello later expressed his frustration that the decision had been made without his consultation.
When Beckham was asked whether the captaincy should be decided by the coach or the FA, he backed the manager.
"Coach's call. You know I think that's always the case," Beckham said.
"Obviously a decision was taken... to take the captaincy away from John. Going forward, I'm sure the captain will be picked by whatever manager steps in."
Beckham, who has not given up hope of being recalled to the England squad even after Capello said last year he was too old for international duty, also reiterated his preference for an Englishman to run the national team.
Beckham offered his support to Tottenham Hotspur manager Harry Redknapp, who has emerged as one of the front-runners for the job.
"Harry's a great man, great manager. His man management is incredible," Beckham said.
"I know players, obviously, who have played under him. I've trained under him. He's not just a great manager but he's a great person as well."
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