Having lost the first-leg of the tie at the Emirates 3-1, the Gunners went out on away goals. The result means they've now fallen at the Round of 16 stage five seasons in a row, losing to Bayern Munich twice, Barcelona and AC Milan in the previous years.
However the latest will be perhaps the hardest to take with Arsenal widely expected to advance against a team sitting fourth in Ligue 1 and shorn of former stars James Rodriguez and Radamel Falcao over the summer.
In the aftermath of defeat, there were conflicting views on whether Arsenal deserved to be eliminated with manager Arsene Wenger viewing it differently to his players.
When Wenger was asked if his team should be out, he replied: "I don't believe so.
"If you look at the number of shots on target they had you will be surprised. Every defeat hurts but we didn't lose."
Monaco 0 Arsenal 2 player ratings
Monaco 0 Arsenal 2 player ratings
1/24 MONACO Danijel Subasic
Looked suspect as Arsenal started to pepper his goal. Giroud made sure he got in the keeper’s face a number of times to distract him. Did enough in the end. 7/10
A quite poor display from the Brazilian. He struggled to contain Welbeck in the first half and Walcott in the second. 6
He was left to deal with Ozil and he did that job with relative ease. 6
4/24 Aymen Abdennour
An assured performance up against Giroud. Strong and positioned himself well 7
5/24 Layvin Kurzawa
Similar to the first leg, he never stopped charging forward. He was quick enough to track back and defend too. Didn’t close down Ramsey for Arsenal’s second goal. 6
6/24 Nabil Dirar
On the counter-attack he was very dangerous for Monaco but should have taken advantages of his chances better than he did. 6
7/24 Jeremy Toulalan
Back from injury and Monaco’s captain organised his midfield well. He won the majority of his battles with Cazorla. 7
8/24 Geoffrey Kondogbia
He was strong and intelligent but after he was booked early in the second half he lacked intensity. 6
9/24 Anthony Martial
Subbed after 58 minutes and didn’t play anywhere near as good as he did in the first leg. 5
10/24 Joao Moutinho
The creative midfielder showed again why Tottenham should have taken a chance when they were interested. 7
11/24 Dimitar Berbatov
Held the ball up well and tried to get a shot off whenever possible. Replaced by Silva on 68 minutes. 6
12/24 From the bench: Yannick Ferreira Carrasco
Showed a lot of energy when he came on. 7
13/24 ARSENAL: David Ospina
Colombian had precious little to do as the vast majority of the match took place in Monaco’s half. His poor display in first leg ultimately proved costly. 6/10
14/24 Hector Bellerin
Spaniard has impressed in recent weeks and put in a steady performance. Accomplished in defence and got forward to provide crosses from flank. 8
15/24 Per Mertesacker
Has not enjoyed his best season but marshalled backline well - not that that kept him overly busy. Slow to push up as Driar was harshly given offside. 6
16/24 Laurent Koscielny
Volleyed against bar when called offside and offered imposing threat at set-pieces. Made vital last ditch challenge on Ferreira-Carrasco. 7
17/24 Nacho Monreal
Offers more defensively than Gibbs and did not lack for effort as Monaco reorganised. His cross ultimately led to Ramsey’s goal but he tired near the end. 7
18/24 Francis Coquelin
Fortunate to escape booking after sliding in on Moutinho. Broke up attacks with ease to initiate Arsenal attacks. Sacrificed for Ramsey. 7
19/24 Santi Cazorla
Volleyed effort blocked by Wallace but unable to greatly influence from deeper role. Rarely ceded possession and but to no overall result. 6
20/24 Alexis Sanchez
Has shown signs of returning to form and shone in touches. Harshly booked for going to ground in area. Spent a lot of time on the ground. 6
21/24 Mesut Ozil
Did not impress with final ball and swapped shirts at half-time. Freshly attired, forced Subasic to tip free-kick over bar. Shot wide when well placed. 7
22/24 Danny Welbeck
Struggled with touch early on but fine ball for opener. Almost added an instant second and forraged to good effect. Replaced by Walcott. 7
23/24 Olivier Giroud
Strong challenge on Abdennour. Headed over bar and struggled with decision making before thrashing rebound for first. Missed late chances. 7
24/24 From the bench: Aaron Ramsey
Came on for Coquelin halfway through second half as Arsenal chased their second - something the Welshman duly provided within 15 minutes. 7
In contrast Per Mertesacker and other team-mates felt Arsenal didn't deserve to have their name in Friday's draw for the quarter-finals.
"The best team went through. Monaco deserved it because they played much better in the first leg," said the World Cup winner.
"We came here and tried absolutely everything. We could have scored more than two. We regret the first game."
Aaron Ramsey, who came off the bench to score Arsenal's second goal, agreed.
“We've always gone out to Bayern Munich and Barcelona at this stage but no disrespect to Monaco, we thought we'd have a good opportunity to qualify.
“But we gave ourselves a tough test from the first leg. It's nearly again, but it's not enough."
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