After the offical UK Kitkat update I removed the camera shortcut from my home screen because I thought I can access to my camera from the lock screen. But now I cannot add the default camera shortcut to my home screen because it's not appearing in the app draver,nor in the disabled applications. However I can start the camera from the lock screen.
Its best you describe your handset type, whether its a Samsung or any other device. I noticed you mentioned that you do not see the camera icon in the app drawer, can you try adding the widget and see whether its there?
Sorry It is a Samsung Galaxy S4. I cannot see the widget in the widget list,however I haven't had any widget for the camera before just the app shortcut in the 4.3 Jelly Bean,but in the Kitkat It disappeared.