Porto, Zenit St Petersburg, Bate Borisov, Apoel and Maribor all made it through to the Champions League group stages on Tuesday night.
Celtic were denied a place in the Champions League proper by plucky Slovenian champions Maribor.
The Glasgow giants had been given a second chance to reach the first-round proper of Europe's top club competition after previous opponents Legia Warsaw were punished for fielding an ineligible player in the third round of qualifying.
Ronny Deila's Hoops earned a creditable score draw in north-east Slovenia last week but, back at Celtic Park, their dreams unravelled as Marcos Tavares' 75th-minute goal earned the visitors a 2-1 aggregate victory.
Earlier on Tuesday, Zenit St Petersburg became the first play-off hopefuls to book their place in the group stages after completing a 4-0 aggregate win over Standard Liege at the Petrovsky Stadium.
Andre Villas-Boas' men doubled their one-goal lead through Jose Salomon Rondon on the half-hour mark and, despite the fact Viktor Fayzulin saw red just before the break, a second-half brace from Hulk made the outcome safe.
Any remote hopes Standard harboured of mounting a last-gasp comeback were ended when Ricardo Faty was sent off just before the final whistle.
Goals from Yacine Brahimi and Jackson Martinez helped Porto dominate Lille at the Estadio do Dragao.
The intriguing tie was finely poised following the Portuguese club's narrow first-leg victory but back on home turf Julen Lopetegui's side were more confident and took the lead through summer signing Brahimi in the 49th minute.
Colombian hitman Martinez struck in the 75th minute to make it 3-0 on aggregate to the 2004 European champions.
Representing Cyprus in Friday's draw will be APOEL FC, who scored four goals past Aalborg without reply to progress 5-1 on aggregate.
Vinicius notched inside two minutes and further strikes from Tomas De Vincenti (43), Stathis Aloneftis (64) and Cillian Sheridan (75) fired the Nicosia outfit well clear of their Danish opponents.
Elsewhere, BATE Borisov were comfortable 4-1 aggregate winners over Slovan Bratislava.
Mikhail Gordeichuk (41) opened the scoring for the Belarusian champions and late goals from Sergey Krivets (84) and Vitali Rodionov (85) put Bratislava to bed.
Guinean striker Seydouba Soumah saw red for the Slovakian club 11 minutes from time.