The Scottish champions were the heavy favourites to progress beyond the third-qualifying round after drawing 1-1 in the first leg.
Sinclair gave Celtic hope with 12 minutes left but AEK held on to win 2-1 and go through 3-2 on aggregate.
"I don't want to make excuses", added Rodgers.
Sevilla are keen on signing Dedryck Boyata from Celtic and are confident they can knock the Bhoys down in terms of their financial demands.
The Celtic fans have taken to Twitter after the game, with Hayes being slammed for a poor performance.
Brad And Angelina Are Butting Heads Again
" Brad and Angelina are not even close to settling their divorce ", the insider told the publication on Tuesday, Aug. 7. Angelina Jolie has reportedly accused her estranged husband, Brad Pitt , of shirking child support payments.
Romania: Tens of thousands protest for second night running
Romania Insider reports that on Friday night, some aggressive protesters, possibly football hooligans, began clashing with police. Late Friday, President Klaus Iohannis, a critic of the left-wing government, condemned "the brutal intervention of riot police".
Messi key to deal, Alderweireld edges closer, Mina move explained
Mina caught the eye for his nation at the World Cup but featured just six times for Barcelona in the second half of last season. Mina is now 8/11 from 7/4 for Old Trafford move with Betway.
Red Star, who have never qualified for the Champions League group stage, will meet Salzburg after the Austrian team strolled into the playoffs with a 4-0 defeat of Macedonians Shkendija.
Striker Griffiths pointed to Celtic winning the domestic treble twice in a row when asked how crucial it was to reach the group stages of European football's elite club competition.
Hoops substitute Scott Sinclair - on for Australia's Tom Rogic - pulled a goal back in the 78th minute but despite a grand finale the visitors could not fashion a second which would have put them through on away goals.
It was the start the Parkhead side had feared and moments later they nearly conceded a second when Victor Klonaridis, who scored in Glasgow last week, burst into the Hoops box but toe-poked a shot wide of the target from eight yards.
Celtic need to wait until Thursday to find out who they meet in the Europa League.
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