Former England captain Beckham made Pearce's shortlist of 35 players but will not be one of three permitted players over the age of 23 picked to compete in the Olympics.
Pearce, who watched Beckham play for Los Angeles Galaxy in the United States last week, picked Manchester City defender Micah Richards ahead of him.
Richards has been included alongside Manchester United midfielder Ryan Giggs and Liverpool striker Craig Bellamy as the three over-age players.
Former Wales midfielder
backed the inclusion of his countrymen Giggs and Bellamy, but criticised Beckham's omission.
"It's appalling. He helped Great Britain get the Olympics," said Savage.
"To have him on the shortlist and string him along, effectively, is quite poor.
"He deserves more respect - he's been a fantastic ambassador for British football and has put the name of Britain across the world. With David Beckham in the Olympic squad, they would have had more of a chance."
"Stuart can kiss goodbye to a knighthood but credit for being brave. He is the manager and should be allowed to pick who he wants."
Former England striker
said Pearce was in a no-win situation.
"He's always been football first and team first, and that's the way he played the game," said the ex-Manchester City player.
"David Beckham has made it difficult for everybody because he has been public about how much he wants to play. It's made it hard for Stuart Pearce and in my eyes, he's more of a man for making that decision."
The British Olympic Association expects to receive the final 18-man squad from the Football Association by early next week.
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