But they were so, so close to making history.
Needing three goals to qualify after that first leg humiliation in London three weeks ago Arsene Wenger’s side almost did it.
No team had ever come back from such a deficit before but they could — and perhaps should — have done.
But Arsenal had left themselves too much to do.
Wenger has many regrets but that 3-1 loss at the Emirates — or specifically the 94th minute goal they conceded when chasing the game — is sure to be one of the biggest.
In the cold light of day Arsenal have now suffered five successive last 16 exits, this another to add to the list of those where they have paid for a woeful first leg performance.
Monaco can now add their name to Barcelona, Bayern Munich (twice) and AC Milan in being sides who have shoved Arsenal towards the European trapdoor before the real contenders have properly begun to warm-up for the stiffest challenges.
It almost goes without saying that Monaco are not in the same class as those other sides. Every side will want to draw them in the quarter-finals.
That Arsenal conceded three against them in the first leg simply goes to show how ludicrously they defended that night.
Dimitar Berbatov and Joao Moutinho are classy players but could do with more support.
This is a functional side rather than an entertaining one.
Well, who really knows what Arsenal are. A fine, improving team that has an overwhelming desire to commit hari-kari, some might say.
They have now won 13 of their last 15 games but the two defeats — at Tottenham and in the first leg of this tie — have been characterised by utterly disastrous performances where they more or less failed to turn up.
There are still a huge number of reasons for genuine optimism, but a top-four finish and an FA Cup victory, both of which are far from certain, may not constitute the improvement many expected after last season.
When Aaron Ramsey added to Olivier Giroud’s first half goal with 11 minutes to go the comeback was very much on.
Yet in front of an eclectic crowd that included Bono and The Edge from U2, they just couldn’t finish it off.
Ramsey’s post-match comments suggested Arsenal had paid a heavy price for complacency in the first leg.
“We have always played Bayern Munich, Barcelona, teams like that and no disrespect to Monaco but we thought we had a really good opportunity of qualifying and we gave ourselves a tough test from the first game,” Ramsey said.
“We came here and have nearly done it but that seems to be the case every year.”
As Wenger had admitted the night before the match, ‘the statistics’ were against Arsenal from the start.
It had been 115 games, over a period of almost four years, since Monaco had last conceded three times at home.
That stat didn’t look likely to change early on as Arsenal started in extremely lacklustre fashion.
Joao Moutinho shot over before Arsenal created a chance, Giroud heading Hector Bellerin’s cross just wide.
The visitors improved, Laurent Koscielny hitting the bar having already been flagged offside, but Arsenal were labouring slightly, lacking that element of luck they needed.
That changed some nine minutes before the break. It was a fine move as Danny Welbeck’s pass found Giroud. The striker’s attempted chip was saved by the advancing Danijel Subasic but hit the Frenchman in the face and fell perfectly for him to find the roof of the net.
It could have been two when Welbeck’s shot hit a prone Aymen Abdennour and the ball spun agonisingly wide of the post.
Monaco were suddenly on edge, ceding possession far too easily and sitting too deep.
Alexis Sanchez was booked for going down too easily when challenged in the penalty area, but the mood of the tie had changed.
Welbeck’s pace was frightening Monaco and his cross flicked off Abdennour and hit Giroud when more meaningful content would have resulted in a goal. The pattern continued in the second-half. Ozil — who swapped shirts with Kondogbia at half-time, much to the outrage of social media — hit a free-kick that forced Subasic into a fine save.
Monaco were reduced to pumping long balls towards Berbatov to release the pressure and Arsenal swarmed forward.
Ozil came within inches of doubling the lead with a half-volley from the edge of the area but it was only when Ramsey scored, thumping home from the edge of the area — they truly began to believe.
Giroud came close but it was not enough. At the end Ozil slumped to his knees and buried his head in the turf.
It was a familiar story. So near, yet so far.
Another glorious failure.
MONACO: Subasic 7, Fabinho 6, Wallace 6, Abdennour 6, Kurzawa 5, Toulalan 6, Kondogbia 7, Joao Moutinho 7, Dirar 7 (Elderson, 87; 6), Martial 5 (Carrasco, 59; 6), Berbatov 6 (Bernanrdo Silva, 69; 5).
ARSENAL: Ospina 7, Bellerin 7, Mertesacker 7, Koscielny 7, Monreal 8 (Gibbs, 83; 7), Coquelin 7 (Ramsey, 63; 7), Cazorla 7, Ozil 7, Welbeck 8 (Walcott, 71; 6), Sanchez 6, Giroud 7.
Referee: Svein Oddvar Moen (Norway)