Sampdoria crashed out of the Europa League qualifiers despite beating Vojvodina 2-0 away from home, with a 4-0 defeat in their first meeting doing the damage.
Goals in each half from Eder and Luis Muriel halved the overall deficit but were not enough to keep the Serie A side's campaign alive.
Saint-Etienne slumped to a surprise 2-1 reverse at home to Romanian minnows Targu Mures, though a 3-0 win away from home saw them through regardless and they will be joined by fellow Ligue 1 side Bordeaux, who beat AEK Larnaca 4-0 over their two outings.
There was mixed emotions for the Belgian sides in action, as Sporting Charleroi were comfortably swept aside by Zorya, while Standard Liege cruised past Zeljeznicar.
Although Vitesse found themselves in trouble against Southampton, Eredivisie rivals AZ had few problems against Istanbul Basaksehir, who were joined in being dumped out by compatriots Trabzonspor, losing rather humiliatingly 2-1 on aggregate to Rabotnicki of Macedonia.
However, Athletic Bilbao, Rubin Kazan, PAOK, Krasnodar, Hajduk Split, Belenenses, Legia Warsaw and Rosenborg all avoided shocks in order to progress.
Odd, Qabala, Zilina, Vaduz, Czech pair Jablonec and Slovan Liberec, Kairat, Rheindorf Altach, Dinamo Minsk and Omonia Nicosia also prevailed, securing playoff places.