Roma crashed out of the Champions League before the group stage following two more red cards in a 3-0 home defeat to Porto on Tuesday.
After Thomas Vermaelen had been sent off in the 1-1 first leg, Daniele De Rossi and Emerson followed in Rome as Porto advanced to the group stage.
Felipe opened the scoring in the eighth minute, heading in a free kick at the far post.
De Rossi, starting at centre-back in place of Vermaelen, was dismissed in the 39th minute for a clumsy tackle on Maxi Pereira, who could not continue and left with an injury before half-time.
His replacement Miguel Layun gave Porto breathing space with a second-half goal, rounding the keeper on a breakaway and scoring from the side of the box.
And two minutes later, Layun's fellow Mexico international Jesus Corona added another goal with a near-post strike to complete the 4-1 aggregate win.
Celtic barely held on to a three-goal advantage from the first leg to advance despite losing 2-0 at Hapoel Be'er Sheva.
Craig Gordon's save of Maharan Radi's poorly taken penalty in the 15th minute proved crucial as the Israeli side struck back but could find a third goal against Brendan Rodgers' men, who advanced 5-4 on aggregate.
Substitute Ben Sahar headed the Israeli champions ahead on the night in the 20th minute and the rattled Hoops were two down on 48 minutes when a mix-up between Saidy Janko and Gordon allowed Romania international Ovidiu Hoban the easiest of chances from a yard out.
Monaco defeated Villarreal 1-0 with Fabinho's late penalty to move on with a 3-1 aggregate win.
Villarreal keeper Sergio Asenjo nearly allowed Thomas Lemar's shot to slip through his legs in the first half but gathered the ball off the line.
The Spanish side nearly found the goal they needed through Santos Borre in the 40th minute, but Danijel Subasic made a good save and when Borre seemed certain to tap in the follow-up, defender Jemerson was able to clear.
Mateo Musacchio handled the ball in the box in stoppage time and Fabinho secured the win with the game's only goal.
Dundalk came up just short of progressing but settled for a 1-1 draw at Legia Warsaw.
Trailing 2-0 from the first leg, Robbie Benson brought the Irish champions back in it with a smashing volley in the 19th minute.
And there was more hope as Adam Hlousek was sent off for a second yellow midway through the second half.
But Dundalk could not find an equaliser and Michal Kucharczyk scored for the hosts in stoppage time to seal the Polish champions' spot in the group stage, 3-1 on aggregate.
Meanwhile, Ludogorets Razgrad held hosts Viktoria Plzen to a 2-2 draw to advance 4-2 on aggregate.
In the seventh minute, Michal Duris scored for Viktoria at the near post following a corner, but the Bulgarian champions hit back with an away goal from Virgil Misidjan, who was played through on goal and shot between the legs of onrushing keeper Matus Kozacik.
Ales Mateju put in a header in the second half to again bring the hosts back in contention, but they would have needed two more to advance, and Claudiu Keseru scored late on for Ludogorets to settle matters.