The trio ignited English football in the 90s as part of Sir Alex Ferguson’s golden generation – including the Neville brothers – but the Welshman never got his chance in a big tournament.
Stuart Pearce selected Giggs and Tom Cleverley from the Reds, and Manchester City’s Micah Richards completes the over-23 along with Craig Bellamy.
But there was no room for LA Galaxy’s Beckham in the 18-man squad, leaving Paul Scholes, along with many, dissatisfied.
"It's a shame about Becks," Scholes told MUTV. "It's surprising as well, after everything David did to help London get the Olympics.
“That's Stuart Pearce's decision, but I feel sorry for David as I'm sure he'd have loved to have played in it."
United veteran, and recently crowned the best player of the Premier League’s 20-year history, Giggs is set to shine after taking the armband.
"From speaking to Ryan, I can tell he’s looking forward to it," Scholes added. "I hope they do well. I don’t see any reason why they won’t do as they’ve got a very good squad.
“Obviously there are other squads in it who want to win the gold medal but I’m sure Ryan will lead the team well and hopefully they’ll go a long way in the tournament.
"Ryan's been unfortunate as Wales didn't manage to qualify [for a World Cup or European Championship] whilst he was playing for them.
“So it’s a good chance for him to play in a big tournament. I just hope they can do well and go all the way and win it."