The LA Galaxy midfielder revealed last week that Team GB head coach Stuart Pearce had opted not to hand him one of the three permitted over-23 slots for the London football tournament, with Ryan Giggs, Craig Bellamy and Micah Richards chosen instead.
Beckham was England captain during Eriksson’s reign, and the Swede believes the former Manchester United and Real Madrid star should have been afforded a space whatever the circumstance due to his status.
"I would have picked him, put him on the bench at the very least," the 64-year-old told BBC Radio Five Live. "He is an icon, he should be involved in the Olympic Games in some way."
The former Real Madrid man, who has not featured for England since 2009, is now expected to take up an ambassadorial role during the Games after featuring heavily in the successful bidding process.
And Eriksson believes it would be right for the east London-born man to be involved in some sort of capacity.
He added: "I hope he will be involved in some way in the Olympic Games, it's important. It is the Olympic Games, it is Great Britain, it is England, it is London."