Ajax has failed to make it through the qualifiers for the third time in a row as it exited 3-3 on aggregate in the tie of the round against Nice, despite hosting the second leg.
The Eredivisie side - beaten in last season's Europa League final - fell behind to Arnaud Souquet's early goal, but Donny van de Beek and Davinson Sanchez struck either side of half-time to turn the match around in its favour.
But a sensational assist from in-demand Nice midfielder Jean Seri, who backheeled a cross for Vincent Marcel to finish well with 11 minutes to go, ensured the Ligue 1 side go into the play-offs.
Young Boys lost the first leg 3-1 in Kiev, but a Guillaume Hoarau penalty gave the Swiss outfit hope, with Jordan Mvula Lotomba scoring the decisive goal in the 89th minute, the teenager's header squirming through the hands of goalkeeper Maxim Koval to send them through on away goals.
RB Salzburg's wait to reach the group stage of the UEFA Champions League goes on after it was eliminated on away goals, a 0-0 draw at home proving enough to send Rijeka of Croatia into the next round.
Steaua Bucharest overturned a 2-1 first leg deficit against Viktoria Plzen with a crushing 4-1 win, but its fellow Romanian, Gheorghe Hagi's FC Viitorul, went out 4-1 on aggregate to APOEL, which scored three times in extra time to settle the tie.
Emmanuel Adebayor was on target as Istanbul Basaksehir beat Club Brugge 2-0 at home to progress 5-3 overall, while Bibras Natcho scored the only goal as CSKA Moscow downed AEK Athens 3-0 on aggregate.
Hapoel Beer-Sheva of Israel went through on away goals despite a 3-1 loss at Ludogorets that saw both sides reduced to 10 men and Slavia Prague also made it into the play-off round on away goals after losing 2-1 at BATE Borisov.
Poland's Legia Warsaw lost 3-2 on aggregate to Astana despite a 1-0 home win, while an injury-time Marcos Tavares goal gave Maribor their second 1-0 success against Hafnarfjordur of Iceland.
A 3-1 win in Serbia had put Olympiacos in a dominant position in its tie against Partizan Belgrade and a 2-2 draw at home was enough to keep the Greek side in the competition.
The draw for the play-off round takes place in Switzerland on Saturday (AEST), with Germany's Hoffenheim, Premier League side Liverpool, Serie A outfit Napoli and Sevilla of LaLiga among the teams entering at this phase of the UEFA Champions League.