No, you probably didn't do anything wrong. When you "move" an iTunes library to an external HDD the original files are not deleted. Once you have determined that the library has been moved successfully and there are no missing files or other problems you might need to solve you can go into ~/Music/iTunes/ and delete the iTunes Media folder. Just make sure you've got everything moved to the external HDD before you delete this folder or you'll lose data.
It's also a good idea to have a backup of the ~/Music folder on another HDD, just in case of emergencies.