Monaco 0 Arsenal 2: Arsene Wenger's side are heavily taxed in Monaco for dodging their duty back in

With members of the Irish rock band in Bono - a bloke who is recovering from breaking an arm in several pieces after a horrific cycling accident - Larry Mullen and the Edge somewhat curiously all watching from the stands on Saint Patrick’s Day, Arsenal lived on the edge before eventually toppling over 3-3 on away goals. U2 were obviously slumming it in the largely tax-free principality having recently endured their own taxing times elsewhere as Arsenal came irritatingly close to a beautiful day among the beautiful people.

Monaco remains a curious little preserve of the filthy rich where one in three residents are apparently millionaires. Yet Arsenal's nouveau riche were left feeling bankrupt when their spirit was exposed to the rawness of this latest nasty exit. Again.

As Bono wonders whether his injury will end his guitar playing, Arsenal's lead man Wenger must think he is destined to end his days at the Emirates never orchestrating the London club's rise to a first Champions League trophy.

Since Barcelona did for them in the last eight in 2010, Arsenal have lost five straight matches at the last-16 stage. They appear to enjoy finding fresh ways to depart football's ultimate event.

There are certainly more reassuring places in the world to be left dispossessed than Monte Carlo.

On a pitch built on top of a car park, Arsenal could not get themselves out of a traffic jam, a pile-up they had engineered back in Blighty with a right old mess of a performance in collapsing 3-1 at the Emirates Stadium three weeks ago. Arsenal dug themselves into a hole deeper than Holloway Road tube station, but the second leg was an excavation assignment of epic proportions. By Jove, was this a narrow miss.

No team in Champions League history had overturned a two-goal deficit from the home leg. It should have been Arsenal. Wenger's side turned a 3-1 loss at the Emirates three weeks ago into a 2-0 win in the principality. It should have been 3-0. At least. 4-0 would have been around even par for the Premier League side on the night.

Unlike the locals, Arsenal paid a heavy tax for dodging their duty in London last month. Arsenal left the land of casinos having their pockets fleeced despite the best efforts of Santi Cazorla, who seemed to spend most of the night trying to deconstruct opponents who would have ended up in the local harbour if they had dropped any deeper. Cazorla was given the run of the place in winding up with the most touches of any Premier League player in a Champions League match since 2009.

145 - Santi Cazorla had 145 touches tonight; the most by a player for an English club in the CL since November 2009 (Mascherano). Control.— OptaJoe (@OptaJoe) March 17, 2015

Glorious failure, and all that jazz. The nature of this one will sting for some time because Monaco seemed hellbent on handing over their right of passage in this competition to an Arsenal lot who produced a herculean effort that was undermined only by their lack of finesse in the final third.

Monaco were as poor as they were impressive three weeks ago. Theirs was a performance that belied their reputation as a team built on stout, sensible defence. Monaco had not lost three goals at their crib since 2011, but they were as fortunate to progress as a gambler winning big at Casino Royale. Fourth in Ligue 1 having shipping a measly 12 goals in 28 outings, Monaco just about staggered through with their survival instincts intact.

Unconvincing, twitchy and error-strewn, Monaco were ripe for the eating - and would have been devoured if Arsenal had taken just a little more care in front of goal. If only they had not self-imploded on their own patch. If only.

When you are chasing an unlikely 3-0 win to keep alive the dream of a first Champions League quarter-final in five years, there is no point in pursuing the joys of self-containment.

The road to perdition was set in stone long before the sojourn to this little haven.

After one awful miss in the first leg, Olivier Giroud enjoyed a night of redemption in his homeland. He scored the first goal with a spot of opportunistic finishing in the first half, and almost rattled the winning goal into the rigging with 12 minutes left when he and Alexis Sanchez seemed to collide in the Monaco area enabling the goalkeeper Danijel Subašic to make a desperate save with the ball almost behind his line.

4 - Arsenal are unbeaten in their last four CL Last 16 second leg matches (W3 D1) but have been eliminated each time. Heartbreak.— OptaJoe (@OptaJoe) March 17, 2015

In between, substitute Aaron Ramsey slammed a low shot into the corner of the net after Monaco had continued to commit hara-kiri.

Arsenal can take solace from a much more measured performance. If they can avoid such evenings as the soulless loss to Monaco in London, they also know that the end of season contains some tangible garlands with the top four and the FA Cup viable targets. Yet that feels like small compensation.

A few weeks ago in these parts, Prince Albert of Monaco saw Martin Murray bashed up by the imperious middleweight world champion Gennady Golovkin in 11 tortuous round near a local casino. It was the same last night. Only Monaco survived. Arsenal are more cruiserweight than true heavyweights when it comes to such regal evenings.

Prince Albert celebrated with an obvious sense of relief. His side join football's royalty when the quarter-final draw is made in Nyon on Friday.

Arsenal ultimately have been cast aside as paupers again when the going gets tough. The fans who sung “one more for Arsenal” as their side attempted to finish the climb should consider whether or not they can keep taking this from Wenger. Is the French coach deserving of one more?

Finishing inside the top four and winning the FA Cup should not be regarded as reasons to get the bunting out for a season that promised to much when Alexis Sanchez signed on from Barcelona last summer. Is failing to challenge for the title an act of wisdom when you study how errant Chelsea and Manchester City have suddenly become? Arsenal are surely too far off them to strike on stunned prey.

It is funny how football continues to bring a sense of earthy familiarity. For all his milions, Prince Albert rejoiced inside a promo jacket that wouldn't have looked out of place on Graeme Souness back in 1992 or Barry Fry nowadays.

The Arsenal captain Per Mertesacker spoke with brutal and admirable honesty in his assessment.

"The best team went through. Monaco deserved it because they played much better in the first leg. We came here and tried absolutely everything. We could have scored more than two. We regret the first game."

Or to name a U2 album, all that you can’t leave behind.