Irish duo Sligo Rovers and St Patrick's Athletic tumbled out of the Europa League, while Palermo, Mainz and ADO Den Haag were also knocked out.
Sligo appeared to have given themselves a chance of reaching the play-off round after holding Vorskla Poltava to a 0-0 draw away from home in the first leg.
However, the Ukrainian side proved too strong in the return after recording a 2-0 success to reach the next stage.
The task for St Patrick's was more difficult after a 2-0 defeat away to Karpaty Lviv and a 3-1 home loss ensured a 5-1 aggregate scoreline.
Evan McMillan had drawn St Patrick's level on the night after Sergei Zenjov's opener, but Karpaty scored again through Ihor Khudobyak and Igor Oschypko.
Palermo were a high-profile casualty after the Serie A side drew 1-1 away to FC Thun, which enabled the Swiss outfit to progress on away goals after a 3-3 aggregate scoreline.
Bundesliga side Mainz are also out after a 1-1 draw away to Gaz Metan Medias produced a 2-2 aggregate scoreline, with the Romanians eventually winning 4-3 on penalties.
ADO Den Haag also bit the dust after failing to overturn a 3-0 first-leg deficit against Omonia Nicosia, but fellow Dutch outfit AZ Alkmaar advanced at the expense of Jablonec.
Atletico Madrid, the 2010 Europa League winners, are into Friday's draw for the play-off round after Jose Antonio Reyes was on target in a 2-0 win over Stromsgodset secured a 4-1 aggregate triumph.
Rennes are also in the hat after a 7-2 aggregate win over Olimpi Rustavi, while Red Star Belgrade thrashed FK Ventspils 7-0 at home to record a 9-1 aggregate victory.
Both Levski and Lokomotiv Sofia crashed out on penalties, but the likes of AEK Larnaca, Dinamo Bucharest, Aalesunds and Club Brugge made it through.
SV Reid knocked out Brondby on away goals as Bursaspor, PAOK Salonika, Maccabi Tel Aviv, Hapoel Tel Aviv, Guimaraes, Austria Vienna and Red Bull Salzburg marched on.