Lille and Trabzonspor were both eliminated from Champions League Group B after playing out a goalless draw while CSKA Moscow beat group winners Inter Milan to qualify.
Lille went into the match needing a win and produced a first-half onslaught but a spirited rearguard action, led by goalkeeper Tolga Zengin and defender Giray Kacar, kept the visitors on level terms.
They were on course to qualify as Inter quickly cancelled out CSKA's opener, but Vasili Berezutski's late goal earned the Russians a 2-1 win and saw them through at Trabzonspor's expense.
Franck Beria and Moussa Sow drew routine early saves from Zengin, while Mickael Landreau was equally comfortable at the other end when Alanzinho shot from 40 yards.
Trabzonspor's Burak Yilmaz lashed a long-range effort over before Eden Hazard beat two men and drew the first serious save of the night from Zengin, who tipped the Belgium forward's drive around the post.
Florent Balmont's attempt sailed wide before Hazard was twice off target from inside the penalty area.
Lille kept up their assault but Payet shot wide before Balmont forced another good diving save from Zengin.
Aurelien Chedjou saw a powerful 12-yard shot blocked by Kacar and Joe Cole fired wide before Trabzonspor lost Ondrej Celustka to injury, Adrian Mierzejewski taking his place.
Cole's corner narrowly eluded Moussa Sow with the goal gaping before Kacar, who had also made a crucial tackle to deny Beria a sight of goal, again rescued the Turks with a brave block from Cole before the half petered out to a goalless conclusion.
Zengin parried Hazard's drive early in the second period, Sow unable to capitalise on the rebound.
Trabzonspor began to look more confident, doubling up on the dangerous Hazard and enjoying more possession, though with few clear-cut chances.
Mathieu Debuchy's powerful drive was blocked by Kacar and Didier Zokora kept out Cole, but Lille were largely kept at bay.
Mierzejewski curled wide after good work by fellow substitute Paulo Henrique, before Burak Yilmaz's effort from a narrow angle - with the Brazilian better placed - was tipped around the post by Landreau.
Payet's shot foundered on the defensive rock that was Kacar and Sow shot wide - but news of CSKA's late winner meant the goalless scoreline was not enough for the Turks.
Many of the fans thought they had mustered the late winner they needed, but Mierzejewski's stoppage-time free-kick in fact found only the side netting.