Arsene Wenger's side managed to hold on despite being reduced to 10 men -- like the first leg when Aaron Ramsey was red-carded -- after Mathieu Debuchy was sent off for a second bookable offence in the second-half yesterday.
"We produced the performance we wanted -- on the tactical side, on the technical side, and on the mental side," said Arsenal manager Arsene Wenger, who may still have to sign a striker as Frenchman Olivier Giroud will be out for up to four months after undergoing surgery on a broken tibia.
His Besiktas counterpart, the former Croatia national handler Slaven Bilic will have to content himself with the Europa League.
"Of course we are gutted, because we played good in both games and are close to qualifying for the Champions League against great opponents," Bilic told Sky Sports.
"Those couple of chances we had to score, but we didn't. Congratulations to Arsenal. They had the experience and quality up front when needed."
A double by Aritz Aduriz -- aided by some woeful Napoli defending -- and Ibai Gomez saw the hosts to victory after Slovakian Marek Hamsik had given the visitors the lead early in the second-half.
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