Benfica were eliminated from this season's Champions League on Tuesday despite coming from behind to beat Paris Saint-Germain 2-1 in Lisbon in their final game in Group C.
Edinson Cavani gave the visitors the lead at the Estadio da Luz only for Brazilian forward Lima to level from the penalty spot before half-time.
Nicolas Gaitan then scored what proved to be the winning goal for the Portuguese giants in the 58th minute, but the final outcome was academic as Olympiakos got the victory they required in the night's other Group C game.
The Greek side beat Anderlecht 3-1 in Piraeus and advance to the last 16 due to their superior head-to-head record against Benfica, twice winners of the European Cup in the 1960s.
"The most important thing was that we did our job to maintain hope of qualifying, but it is a shame to miss out because PSG and Benfica were the two best teams in the group," insisted Benfica coach Jorge Jesus.
PSG, meanwhile, had already sealed their progress as winners of the section before this game, and their coach Laurent Blanc was therefore able to leave Zlatan Ibrahimovic and Thiago Silva behind in Paris along with suspended duo Marco Verratti and Gregory Van der Wiel.
In their absence, Blanc gave starts to the likes of Zoumana Camara, Javier Pastore, Adrien Rabiot and Jeremy Menez, while there was a debut at right-back for the Malian Kalifa Traore, but Blanc was not convinced by their display.
"I am disappointed with the performance of the team in the second half. For what Benfica did, they deserved to win," he said.
"I hope PSG will be in contention to win the Champions League but there are a lot of matches to play before that. We can't wait for the draw."
Benfica's fate was out of their hands but they showed the greater urgency right from kick-off against a PSG side playing without pressure.
Enzo Perez signalled their intent with a curling effort inside the opening five minutes that was heading for the top corner until Salvatore Sirigu intervened with a fine flying save.
Sirigu then boxed away a Silvio shot, while Gaitan and Nemanja Matic both narrowly missed the target in the opening half hour.
The Ligue 1 leaders had offered little at the other end with the exception of a first-time Menez strike that was stopped by Artur in the home goal.
However, PSG got their noses in front in the 37th minute as Cavani converted his 15th goal in all competitions this season, rolling in a Menez cutback from on the goalline.
Benfica could feel hard done by as Menez may have been offside when Pastore played the initial pass, but the hosts were afforded the chance to draw level just before the break.
Debutant Traore was penalised by English referee Mark Clattenburg for a clumsy challenge on Silvio right on the edge of the area, and Lima confidently beat Sirigu from 12 yards from the resulting penalty.
Buoyed by that, Benfica continued to push forward after the restart, and Sirigu was again called into action to save a powerful shot by Lima.
They went on to take the lead for the first time in the 58th minute, though, Argentine winger Gaitan tucking away the loose ball for his first goal of the campaign after Camara had blocked a Maxi Pereira cross.
Blanc responded by sending on the fresh legs of energetic duo Blaise Matuidi and Ezequiel Lavezzi for the final half hour and the latter nearly levelled midway through the second half, lifting the ball just past the far post from a Menez assist.
Benfica held on, but there were no favours from Anderlecht in Greece, and last season's Europa League runners-up will have to settle for another crack at that competition in the New Year.
PSG, meanwhile, can still dream of returning to the Estadio da Luz for the final in May as their thoughts turn to next week's draw for the last 16.