Ludogorets Razgrad spring Champions League surprise to rub salt into wounds of Rangers
The teams were all-square going into the second leg in Bulgaria after a 1-1 draw in Piraeus, and they could not be separated again after a 2-2 draw at the Huvepharma Arena.
However, Ludogorets prevailed 4-1 on penalties to progress and send the champions of Greece into the Europa League play-off round.
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Hide AdOlimpiacos had taken the lead through Yann Mvila, but a Ruben Semedo own goal and then a Pieros Sotiriou strike put Ludogorets 2-1 up on the night.
Youssef El-Arabi forced the game into extra time with an equaliser before the Bulgarians prevailed on penalties.
FC Midtjylland, the conquerors of Celtic in the previous round, are out of the tournament after a 4-0 aggregate defeat by Dutch outfit PSV Eindhoven.
The Danes needed to overturn a 3-0 deficit from the first leg in Netherlands, but they never looked like landing a blow on their visitors and a 90th-minute strike from Bruma gave PSV a 1-0 win on the night.
Monaco are also safely through to the play-off round. They defeated Czech side Sparta Prague 3-1 in the principality, with Gelson Martins, Alexander Golovin and Sofiane Diop on target. They will face Shakhtar Donetsk next after the Ukrainians defeated Genk 2-1, 4-2 on aggregate.
Red Star Belgrade suffered a surprise exit to Moldovans Sheriff Tiraspol, as did Slavia Prague, who failed to overturn a 2-0 first leg defeat by Ferencvaros.
Swiss side Young Boys are also in the play-off round, defeating Cluj 3-1 in Berne (4-2 on aggregate).