The solution? Reinstall 8.1
I had the same problem: 8.1.1 drains the battery of my iPhone 4s. The installation had turned on 'push' for emails, and possibly a lot more. Did all tricks (location services off, refresh apps background off, display manual / dimmed, etc) and even reinstalled 8.1.1 a second time. Made all no big difference, the battery performance remained very, very poor. In a few hours it drains from 100 to 70% or so, without any 'obvious' activity (battery usage will indicate that the iPhone is still active for many hours while asleep, but for no obvious reason).
Yesterday I reinstalled 8.1, overnight the phone only lost 10%, and during the day my phone went from 90 to 84% only. Thus the battery usage is now very good!
My advise: reinstall 8.1 now (for the 4s: the iOS 8.1 firmware, iPhone4,1_8.1_12B411_Restore.ipsw, is still signed by Apple, date 24/11/2014; so it is still possible).