The top 12 teams from the 1984–85 League of Ireland automatically qualified for the Premier Division.
[2][3] After winning the league title in the previous season, Shamrock Rovers received automatic qualification into the first round of the European Cup.
Budapest Honvéd were the hosts for the first leg and won the game comfortably in a 2-0 defeat of Shamrock Rovers.
In the return leg, Shamrock Rovers were defeated once again 3-1, thus eliminating them from the competition.
In the second leg, United were defeated 3-2 at Terryland Park, ending their European campaign.