That means they could face Tony Bloom’s Scottish interest Hearts.
Bloom has a 29% share in the Edinburgh club, who came through a penalty shoot-out with Rapid Vienna after a pair of 2-2 draws.
LaLiga outfit Getafe are a potential pot-three opponent and Albion might come up against Luka Vuskovic’s beloved Hajduk Split.
But they cannot face any of the other pot-two sides, namely Midtjylland, Crvena Zvezda (Red Star Belgrade), Gent, Panathinaikos or Pafos.
Group one sides, in theory the toughest opponents, are Atalanta, Braga, Ajax, Monaco, FC Copenhagen and Freiburg.
In the lower pots, possible opponents include Andorran minnows Inter Club d’Escaldes, surprise Swedish champions Mjallby and Kairat Almaty of Kazakhstan.
There were play-off round exits for Scottish sides Rangers, Motherwell and Hibs as well as Shamrock Rovers and Larne from Ireland.
Potentially enjoyable trips to Vienna, Rijeka and Thessaloniki were also taken off the table.
Albion will play three home games and three away and their results will decide their placing in a 36-team table.
A top-eight finish would see them straight into the round of 16 while ninth to 24th would take them into a play-off.
The bottom 12 in the 36-team league are eliminated.