Battlefield 4 "you must be signed in to origins to access online features"

You need to sign in to origin itself.  Origin is needed in order to play the game. 

Here's a link to Origin, you'll need to download it and sign in.  https://www.origin.com/en-us/store/

Origin is the digital service that EA uses for its games. It's very similar to Steam in which you can buy games, DLC's, etc.  Origin is used to by the developer to update the game as well.