It seems that, if I upload an image from my computer then the Featured Image option works, but if I want to select an Image from any URL as a Featured Image, that doesn't work! It is a sad news for me. Because due to space shortage, I always upload the images in Picasa and then use the image URL to show it in my posts.
So as a default theme of WordPress, if Twenty Eleven supports the Featured image from web url as well, that would be great!
Hopefully, it will be implemented soon.