A couple of ways to do this:
1. using the eject button that appears next to the icon in the sidebar. I guess this is the one you mentioned.
2. Right click on the icon on the desktop and choose Eject from the menu that appears.
3. Drag the icon into the trash. Note that the trash icon changes to an Eject icon when you start to move the device's icon.
4. Select the icon and find Eject in the menubar at the top of the screen.
Once the icon goes away, you can remove the drive.
Your other problem could be a number of things. Usually it is an indication that there is a file/application, that lives on that drive, that is still open. Make sure that all applications are closed and it "should" eject.
Also, I think you will find that the message you got said that you "could" damage the data on a drive that was just pulled out. Not that you DID damage it.
For some reason, I can't remember how to safely remove a CD or USB flashdrive, etc, I know "eject" is in there someplace, but the rest I'm not sure of. I currently have two flash drives plugged in. When i was done looking at them, I looked in Finder and found the little house/arrow thing. I clicked one and the f/d icon on the desktop disappeared, but the lite on the f/d is still slowly blinking. (i'm not sure what it was doing before). When I tried to do the same thing to the other one, it keeps telling me it's in use, and to close it. I can't seem to do that to it's satisfaction. It's lite is alternating between solid and flashing 5 times. They are different brands.
But this question is really generic, because I had something else that told me that I'd damaged it by removing it too soon.