A rapidly draining battery following an IOS upgrade process is usually a sign that a corruption or rogue setting on your device is causing a panic. The best way to resolve this is normally to back-up, do a clean restore of 5.1 to the device, and then restore your data via iTunes or iCloud (whichever you are using).
If the problem persists after that, the issue may lie with data in your backup, so you may need to consider a fresh restore and start again from scratch.