The flashing light uses very little power as compared to the wifi or cell tower radios. It is doubtful that the small LED light you are seeing is responsible for the battery drain.
To find out what is really draining your battery, open the settings page on the phone and click on the line that says battery. That will show you what has been using the largest portion of your battery.
The fix from there depends on what is causing the battery drain.
If you are certain that this LED flashing light is causing the drain, go to Settings – My device – LED indicator. From there you can choose your notification options.
There is an app on Google Play called NoLED that may also help you set up the LED light, or stop it from coming on at all.