I have similar question that was posted earlier in No application keys for Azure Mobile Apps - what's a simple replacement?. But there doesn't seem to be any satisfying answer on that issue.
I just want to restrict the access to the the azure custom api & db tables with a simple key/code in my mobile client application. I dont want the users to be forced to login to their fb/google etc accounts. The "new" app service/mobile app seems only to work with authentication where the user/client sign in using google/fb . Is there any way to accomplish the "old" application key behaviour in this "new" app service?