Italian side Roma failed to reach the Champions League group stage after having two men sent off in a 3-0 second-leg defeat by Porto.
Roma were the favourites after drawing 1-1 in Portugal, but went behind when Felipe gave the visitors an early lead.
They imploded as Daniele de Rossi and Emerson Palmieri were shown straight red cards either side of half-time.
Miguel Layun slotted in Porto's second, before Jesus Corona turned his marker to add the third moments later.
Roma are the third Serie A team in successive years to lose in the play-off round, leaving Juventus and Napoli to represent Italy in Thursday's group-stage draw.
Elsewhere, Celtic survived a second-leg onslaught against Israeli side Hapoel Beer Sheva to reach the group stage for the first time in three seasons.
Dundalk were unable to become the first Irish side to qualify as they lost 3-1 on aggregate to Legia Warsaw, while Monaco beat Villarreal 1-0 as a late penalty by Fabinho sealed a 3-1 aggregate win.
Bulgarian side Ludogorets joined them in the next phase by drawing 2-2 at Czech hosts Viktoria Plzen to progress 4-2 on aggregate.