Arsene Wenger's men kept up the pressure throughout the evening, with Olivier Giroud and Aaron Ramsey scoring late in each half, but paid for their poor performance in the home leg
Arsenal narrowly missed out on a Champions League miracle as their 2-0 win at Monaco was not enough to prevent them from exiting the competition on away goals.
Needing a 3-0 victory to guarantee a spot in the quarter-finals, the Gunners pushed throughout and finally got the breakthrough shortly before half-time when Olivier Giroud fired into the roof of the net.
Though Monaco fought hard to hold them off, Arsene Wenger's men looked likely to score again and did so with just over 10 minutes to go, substitute Aaron Ramsey burying a second when a disastrous clearance went straight to him after Theo Walcott hit the post.
Arsenal could not scramble their way to a second, however, and are left lamenting the first-leg failure that put them up against it in this game.
Wenger's side have now exited the competition at the first knockout round in each of the last five seasons while Monaco progressed to the last eight for the first time since 2004, when they went on to reach the final.
Monaco's ultimately successful plan to soak up wave after wave of Arsenal pressure became immediately evident, and the visitors' first chance came as Giroud headed Hector Bellerin's right-wing cross wide of goal.
As Arsenal continued to press forward, Laurent Koscielny struck the crossbar from close range as Monaco failed to deal with a free kick but the linesman's flag was raised for offside in any event.
Giroud broke the deadlock nine minutes before the interval, smashing the ball into the roof of the net at the second attempt after his initial effort was smothered by Danijel Subasic.
Arsenal almost had a second two minutes later but Danny Welbeck's goalbound shot struck a prone Aymen Abdennour and squirmed wide of the right-hand post, before Alexis Sanchez tripped himself up in the penalty area, resulting in a harsh booking for diving.
In first-half stoppage time, Giroud and then Welbeck both threatened to double the visitors' lead as Arsenal went into the break in the ascendancy.
Arsenal continued to look the more threatening after the interval and Mesut Ozil saw a free kick tipped over by Subasic, before fizzing a half-volley wide from just inside the area.
Arsenal felt they should have had an indirect free kick when Subasic handled Fabinho's backpass but the referee deemed the defender's intervention to have been unintentional.
With 11 minutes remaining, Ramsey gave Arsenal further hope with a fine right-footed finish. Fellow substitute Walcott saw his initial shot come back off the post and, when Layvin Kurzawa's poor clearance fell straight to Ramsey, the Welshman rifled a shot low into the bottom-left corner.
As Monaco wobbled, Subasic produced a fine save to claw out Sanchez's header at the far post, his crucial intervention sending the hosts through despite a first defeat on home soil in Europe this term.
