Başakşehir had a 2-2 tie with Sevilla on the second leg of the playoff round but the 2-1 defeat in the first round advanced Sevilla into the Champions League group stage.
Başakşehir started the match at a fast pace, finding the net in the 17th minute from first-leg scorer Eljero Elia. The Dutch winger slid in Junior Caicara's low ball to give Başakşehir the lead.
The second half was to be a different story, as Sevilla equalized and gained the upper hand when Sergio Escuredo brushed aside his marker to score a header in the 52nd minute.
The La Liga side then took a commanding lead in the 75th minute with Wissam Ben Yedder's low driven shot beating Başakşehir goalkeeper Volkan Babacan after a counter-attack.
Başakşehir increased their tempo in the last 10 minutes before Edin Visca restored the Istanbul club's morale when he crashed home a powerful shot in the 82nd minute.
But the Istanbul side's last-minute heroics were not enough as Sevilla managed to draw 2-2 and move on to the group stages.
Başakşehir will now continue its European campaign in the Europa League.
LATER TUESDAY IN PLAYOFF ROUND (first leg scores in parentheses)
Maribor (1) vs. Hapoel Be'er Sheva (2)
Nice (0) vs. Napoli (2)
Rijeka (1) vs. Olympiakos (2).
