Beckham played for Capello at Real Madrid and understands the 65-year-old's decision to step down in the wake of John Terry's removal as England 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," the LA Galaxy midfielder told reporters.
"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."
When asked who should decide the fate of the national captaincy, Beckham responded: "Coach's call. I think that's always the case.
"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."
Harry Redknapp is the overwhelming favorite to become the next England coach and Beckham believes that he would be perfect for the role.
Since his move to the United States, Beckham, England's most capped outfield player, has spent two winters training with Tottenham in a bid to maintain fitness and was reportedly close to sealing a temporary move to White Hart Lane this January.
"Harry's a great man, great manager. His man management is incredible," Beckham said.
"I know players, obviously, who have played up him. I've trained under him. He's not just a great manager but he's a great person as well."