CSKA, 2005 UEFA Cup winners, lost 2-0 to the Swedes who knocked out the Russians 2-1 on aggregate after Kwame Karikari grabbed an early goal for the visitors and Martin Lorentzon added a second in stoppage time.
Elsewhere, most of the favoured teams made it through to the next round.
Inter Milan secured a 2-2 draw against Romanian side Vaslui to progress 4-2 on aggregate despite going down to 10 men after goalkeeper Luca Castellazzi was red-carded in the 33rd minute following a foul on Liviu Antal.
Marseille survived a goalless draw with Moldovan side Sheriff, going through thanks to a 2-1 win last week, while Red Star Belgrade went out after a 3-2 defeat at Bordeaux, Yoan Gouffran's penalty sealing victory for the Ligue 1 side.
The Europa League draw takes place in Monaco on Friday.
