Defending champions Atletico Madrid could face Chelsea or Liverpool in the Europa League last 32 after finishing runners-up in Group B to Plzen.
Atletico were beaten 1-0 by the Czechs, who as group winners join the two English clubs among the 16 seeds.
Five places in the knockout stage were available from the final group games.
Tottenham and Liverpool progressed while Steaua Bucharest and Stuttgart advanced from Group E and Basel earned the point needed at Genk to join them.
The 12 Europa League group winners are seeded for the knockout stage draw which will take place on 20 December.
Eight teams drop into the Europa League from the Champions League, all of whom finished third in that competition's group stage.
Uefa's website states that the "four best third-ranked teams in the Champions League group stage" will be seeded.
Chelsea and Cluj are the highest points scorers from the third-placed teams, having accumulated 10 points each, while Olympiakos and Benfica picked up nine and eight points respectively.
Young Boys beat already-qualified Anzhi 3-1 but exited after Liverpool won at Udinese to finish top of Group A.
Lazio thrashed Slovenian side Maribor in a 4-1 away success to win Group J ahead of Spurs, who qualified with a 3-1 home triumph against Panathinaikos.
Atletico, who beat La Liga rivals Athletic Bilbao in last season's final, were downed by Vaclav Prochazka's first-half winner for Plzen.
The Czech side held out to win Group B - and provide the perfect 49th birthday present for coach Pavel Vrba.
Most of the qualification excitement centred around Group E, where both places were still to be decided in the final round of matches.
FC Copenhagen needed to beat Steaua Bucharest to stand any chance of progressing and their task was boosted by the dismissal of Steaua's Cristian Tanase shortly after half-time.
But the Romanians edged ahead through Raul Rusescu's blistering strike before Igor Vetokele nodded in a late equaliser to set up a frantic finish.
The Danes could not find the winner which would have clinched qualification as Stuttgart progressed despite a 1-0 home defeat by bottom-side Molde.
Swiss side Basel earned a 0-0 draw at already-qualified Genk, which meant the visitors advanced from Group G alongside the table-topping Belgians.
The stalemate renders Videoton's tie at Sporting Lisbon, which will be played on Friday after it was postponed because of a waterlogged pitch, irrelevant.
Hannover surrendered a two-goal advantage to draw 2-2 at Levante and top Group L at the expense of their Spanish hosts.