Moto X 1st Gen - WiFi not working after upgrade to Android 5.1
I'm going to recommend you to try 2 things, then if all else fails contact Motorola.


Clear the system cache. Many post-update issues can be fixed with this. It clears out all of your phone's temporary files, and after a update, the cache is usually junked up with all kinds of stuff. This site does an excellent job explaining the process. For users with other devices, a quick Google of clear system cache device name OS will get you what you need.
Factory reset your device. It may seem bit extreme, but it usually gets the job done. Avoid restoring from a backup if possible as it may restore the issue as well.


If that doesn't work, Motorola has a decent customer support system, but expect to be on hold a lot. (At least less than Comcast)