Beckham missed out on the squad last month after coach Stuart Pearce did not pick him as one of the players aged over 23.
Beatles musician McCartney has urged Pearce to have a list-minute rethink and include Beckham in the team.
"He's a national hero. I would've thought Beckham would be first choice because of his huge contribution to getting the Olympics," McCartney told Shortlist.
"But some idiot decided otherwise. I feel a bit sorry for the three over 23s, because we're going to be looking at them and saying, 'That should've been Beckham'. He's a national hero, a crowd-puller."
McCartney added: "It would've been great for him to lead out our British football team.
"But some person somewhere said, 'So-and-so's playing better'. Like it matters."
A Team GB source responded to calls for Beckham to be included, saying that Pearce will not change his squad.
"It doesn't matter if Paul McCartney, the Queen and every star in Hollywood has their say," the insider told The Sun.
"Stuart Pearce has picked his team and that's it."
Beckham will be involved at the London Olympics opening ceremony on Friday (July 27), while McCartney is also expected to perform at the event.