It could be the update (if was an OS update) or it could be something else. Have you tried turning it off and then starting it up in "Safe Mode" to see if it drains as fast in there? While you can't use most apps from there, you can make calls and test the battery. I would try that, as the OS runs in there. If the battery lasts longer in there, then it is something else on the phone that is draining it. If it drains fast while in "Safe Mode" then either the update is the cause, or the battery may be in need of replacing.
To get into "Safe Mode" please do the following.
1. First turn off the phone.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.
NOTE: If it doesn't happen in "Safe Mode", then you will need to figure out what app or other item on the phone is the cause.