Arsenal failed to make the Champions League last eight for the fifth straight season despite beating Monaco in the second leg of their last-16 tie.
Needing to score at least three unanswered away goals after a 3-1 defeat at home, they went ahead through Olivier Giroud’s close-range finish.
A lively Danny Welbeck went close to doubling the lead before half-time, but despite Aaron Ramsey coming off the bench to score late on, with Giroud going close again, Monaco held on.
It was a heartbreaking end to Arsenal’s European campaign as they came agonisingly close to scoring the third away goal they needed to progress, a feat never before achieved in the Champions League era.
All over the pitch Arsene Wenger’s side were vastly improved from the defeat at Emirates Stadium last month and they ensured that Monaco conceded their first Champions League goals at the Stade Louis II this season.
Arguably, though, the Gunners lost this tie in the first leg through their defensive fragility, where they conceded a crucial third goal in the 90th minute.
And although they continued their fine form with an eighth win from nine games, that blip in the first leg was enough to ensure Monaco reached the quarter-finals for the first time since 2004.
They join holders Real Madrid, Bayern Munich, Paris St-Germain, Porto and Atletico Madrid in Friday’s draw.
Giroud was among those who were widely mocked in the first game, but after the Gunners withstood early pressure, the French striker was a key influence and combined cleverly alongside the impressive Welbeck.
After he had headed just wide and Laurent Koscielny turned a free-kick onto the Monaco crossbar but was wrongly ruled offside, the visitors established control and could have been at least two goals ahead before the break.
Giroud gave Wenger’s side the lead when he latched onto Welbeck’s through ball and managed to steer his shot in at the near post after Danijel Subasic had blocked his first effort.
Two minutes later Welbeck was unlucky not to join him on the scoresheet when his rasping drive was blocked by the prostrate Monaco defender Aymen Abdennour.
With Welbeck and Alexis Sanchez providing pace and width up front, Arsenal continued to cause problems for the Ligue 1 side as Mesut Ozil went close with a free-kick and flashed another effort wide.
But the hosts, who had one more day’s rest than their opponents, regained their composure around the 60-minute mark and caused some nervy moments in the Arsenal defence before Wenger brought on Ramsey and Theo Walcott in search of a second goal.
It paid dividends as the substitutes combined for Arsenal’s second with 11 minutes left, Walcott striking the post from a left-wing cross before Ramsey got on the end of Layvin Kurzawa’s poor clearance.
Giroud almost tucked in at the back post from a free-kick but perhaps he was guilty in putting off the better-placed Sanchez.
In the end, Arsenal were left frustrated and repeated the same results in their two-legged defeat by Bayern Munich two years ago. This, though, will be harder to swallow.