Sharpe had extended trials at the Galaxy before he eventually signed for the Rapids and has sympathy for Beckham's current situation.
The Aussie told tribalfootball.com: "David is a very well respected player not just around the MLS, but the world, amongst the players, and his move to AC Milan was a fantastic option for him and his international career.
"All the players here at the Rapids agree so.
"In saying that, obviously Galaxy fans are not going to agree as he has a contract there, and there was always going to be some sort of hostile reception for David on his return to LA. But from what we understand, the few fans that he had a little problem with in LA went way over the top with their comments and brought David's family into the taunts. He has the right to get annoyed.
"Becks carries himself so well and no doubt has been through things that none of us could begin to understand, so you can't hold that against him in anyway.
"From my time at the Galaxy, everyone got along well with David. I never saw any animosity between David and Landon (Donovan), but I am only speaking from the short time I was there.
"I got along very well with him from day one and spent quite a bit of time chatting with him at training and in the dressing room, and since then, when we have played LA, he has always come up and said hello for a quick chat."