Aris Salonika went through at Atletico's expense by beating Rosenborg 2-0 to finish second in Group B with 10 points from six games, two ahead of the Spaniards. Leverkusen had already qualified.
"Our team is good enough to have gone further, but we haven't," said Atletico coach Quique Sanchez Flores.
"Now, we have to face the consequences and forget this as quickly as possible. I hope we get back into Europe through the front door, via the Champions League."
Lille and Anderlecht took the only two places which were still up for grabs in the round of 32 on the final night of group stage action.
Lille beat Ghent 3-0, also hitting the post three times, to leapfrog the Belgian side and finish second in Group C behind already-qualified Sporting.
Anderlecht took second spot in Group G with a 2-0 win over Hajduk Split, helped by a brilliant goal from Argentine forward Matias Suarez who beat two players before nonchalantly curving the ball past the goalkeeper. Tom de Sutter opened the scoring.
Anderlecht pipped AEK Athens on their head-to-head record after the Greeks, needing only a draw at home to qualified Zenit St Petersburg, instead lost 3-0.
Atletico, starting level on seven points with Aris but with a worse head-to-head record, dominated the first half against Leverkusen with Uruguay striker Diego Forlan close with a half-volley just before the break.
But they found the conditions difficult, with snow on the surface repeatedly slowing down the orange ball, and appeared to lose heart on hearing that Aris had taken the lead in Greece.
Atletico replied three minutes later when Sergio Aguero held the ball up and laid it on for substitute Fran Merida to sidefoot home with his first touch.
Aguero and Mario Suarez both wasted good chances to win the game for Atletico but it would not have mattered as Aris scored in stoppage time at the end of each half to beat Norwegian champions Rosenborg.
Croatian forward Danijel Cesarec forced the ball across the line at the end of the first half to put former Valencia and Inter Milan coach Hector Cuper's team in front after Sergio Koke's deflected shot hit the crossbar.
Frenchman Ricardo Faty provided the finishing touch, collecting Mattias Bjarsmyr's attempted clearance and driving the ball home with virtually the last kick of the game.