Arsenal qualified for a 17th successive season with a nervy 1-0 win at home to Besiktas and Malmo made it for the first time with a 3-0 win over Salzburg, whose participation ended in the qualifiers for the ninth time in a row.
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Ludogorets centre-back Cosmin Moti, forced to go in goal after keeper Vladislav Stoyanov was sent off, saved two penalties as his team beat Steaua Bucharest 6-5 in a shoot-out to qualify for the first time.
[DEFENDER MOTI GOES IN GOAL FOR CHAMPIONS LEAGUE PLAY-OFF PENALTIES – AND WINS]
Forgotten German striker Stefan Kiessling scored twice to help Bundesliga side Bayer Leverkusen storm past FC Copenhagen 4-0 to complete the line-up.
The group stage draw, featuring only two Italian teams following Napoli's exit, will be made in Monaco on Thursday.
Napoli's defensive nightmare will prove expensive as the group stage earned them around 38 million euros last season in appearance fees, performance bonuses and television rights.
It will also pile pressure on coach Rafael Benitez, whose expensively-assembled side did the bare minimum expected of them last season by finishing third in Serie A and winning the Italian Cup.
Held 1-1 at home last week, Napoli survived a difficult first half before taking the lead immediately after halftime when Marek Hamsik collected a headed clearance on the edge of the area and scored with a low shot into the corner.
But it all went wrong in the 61st minute when Aritz Aduriz escaped his marker at a corner to equalise.
It got worse for Napoli eight minutes later when a long ball out of the Athletic defence was completely misjudged by Raul Albiol, who collided with goalkeeper Rafael Cabral, allowing Aduriz to score into an empty net.
Five minutes later, Unai Lopez's through ball caused more havoc in the Napoli defence and Ibai Gomez nipped in to drill the third past Rafael and seal Atheltic's place in the group stage for the first time since 1998/99.
"We took the lead, but in a few minutes we made some significant mistakes and lost control of the game," Benitez told Sport Mediaset. "We knew it could end up like this, we are all disappointed, but we have to look forward."
Rosenberg struck again with six minutes left as Malmo became the first Swedish club to qualify since Helsingborg in 2000-01.
Ludogorets sent their tie against former champions Steaua into extra-time when Brazilian Wanderson scored with a spectacular shot in the 90th minute to give them a 1-0 win on the night and make it 1-1 on aggregate.
There was more drama when goalkeeper Stoyanov was sent off for a professional foul in the final minute of extra time and, with the Bulgarians having made all three substitutions, Moti went in goal.
Having converted his side's first penalty, Moti saved Paul Pirvulescu's second attempt for Steaua and Cornel Rapa's sudden-death effort as Ludogorets won 6-5 in the shoot-out.
Leverkusen, 3-2 up from the first leg against their Danish opponents, quickly extended their lead.
Kiessling, repeatedly overlooked by Germany despite a prolific scoring record, set up Son Heung-Min to score in the second minute and Hakan Calhanoglu added another with a deflected free kick in the seventh minute.