I don't think you should feel embarrassed at all. I, personally, find it flattering when someone is carrying the same AUTHENTIC bag as I'm carrying. It means we both have great taste!
The ones who should feel embarrassed are the ones who are carrying the fakes...and they know who they are! I can't understand how one carrying a fake designer bag can carry it proudly.
You have a Classic bag! Wear it, love it, show it with pride!!