Beckham made Pearce's initial 35-man shortlist but failed to secure a place in the final 18 as an over-23 pick ahead of Craig Bellamy, Micah Richards and Ryan Giggs.
Rodwell, who himself has been ruled out through hamstring problems, accepts Pearce's decision but feels that he has missed a trick by leaving Beckham out of his squad.
The 21-year-old told BBC Radio 5 Live: "Everyone in the squad would learn from David Beckham. He is a legend.
"I think everyone is a bit surprised but the manager obviously has his reasons. I'd like to have seen him in the squad."
|GOING FOR GOLD?
|6/1||Team GB are 6/1 with bet365 to win the gold medal at the London 2012 Olympics football tournament.|
Meanwhile, former Wales international Robbie Savage has backed the selection of his compatriots Bellamy and Giggs for the Games.
However, he slammed the decision to leave Beckham out, citing the LA Galaxy midfielder's contribution to the London 2012 campaign as reason enough to include him.
Savage said: "It's appalling. He helped Great Britain get the Olympics. 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."