The cup losers only ever get in if they lose the final to the league champions (i.e. double winners). EUFA rank the Cup winners ahead of 2nd in league.
So if, for example, Pats beat galway in the FAI final, and the league table finished as
1 Bohs
2 Pats
3 Derry
4 Sligo
The Euro qualifiers would be (depending on licenses etc etc) Bohs, Pats, Derry. Sligo
Presuming the 1,2,3 in the league is Bohs, Pats, Derry (or Derry/Pats) and Galway lose the semi on Sunday, 4th will be guarenteed Europa League ;)