In the case where the cup winner is already qualified for the CL, the FA Cup Runner-up gets the EL place, but league cup runner-up does not. LFC qualified last season because Portsmouth didn't apply for their European licence in time and therefore defaulted their FA Cup runner-up spot back to the league. Because of all these non-qualified clubs reaching (winning) finals, there was a chance this season that no side would qualify for the EL from the league (if LFC had gone on to win the EL, for eg).
Sides to play in EL next season (likely): Birmingham (league cup winner), Man City or Spurs (EPL 5th), Bolton or Stoke (FA Cup finalist with CL-qualified opponent), Fulham (Fair Play).
We can still qualify for the EL though, as I understand it. LFC must finish 5th, or Man City must finish 5th and win the FA Cup (in which case I believe the league place passes down). I don't think any part of any of these scenarios is likely - City won't win the FA Cup, and Spurs will most likely finish 5th. I hate mathematical chances - relying on them implies the horse has already bolted.