Yep, there has never been a spot on offer for being League Cup runners-up to my knowledge. I don't remember how things were pre-1985, though.
Ian's access list is close to correct. I believe it runs something like this.
1) FA Cup winners
2) Highest Premier League finisher who are not FA Cup Winners or qualified for the Champions League (very usually 5th, on odd occasions something else, like last season when Spurs were in this slot for 4th)
3) League Cup winners
4a) FA Cup runners-up, if FA Cup winners have a place in CL
4b) Any remaining spots go to highest league finishers without a European place otherwise. However, despite having a lower entry priority than the FA Cup runners-up, they will place higher in the eventual order (i.e. this season, Newcastle took a contingency place as the 2nd team qualifying by league position, whilst Liverpool took the FA Cup runners-up spot. Desipte Newcastle only getting in because there was a spot spare, Liverpool begun in the Europa League a round earlier)