After the Blues had fallen 2-0 behind, Leroy Sane looked to have saved the day with a late goal that briefly put City back in front on aggregate.
But the hosts rallied to score a third five minutes later to tie the overall score at 6-6 - enough for Monaco to progress to the last eight on the away goal rule.
It is a crushing blow for a team that had gone 11 games without a loss, but the price of a poor first-half display when City were, at times, overrun by the rampant Ligue 1 leaders.
What happened?
City made four changes from the side that beat Middlesbrough 2-0 at the weekend with Aleksandar Kolarov, Willy Caballero, Fernandinho and Bacary Sagna all recalled to the starting XI.
OUCH: David Silva is sent tumbling by Fabinho
Monaco, meanwhile, were without top scorer Radamel Falcao as they looked to find enough goals to make their three at the Etihad prove decisive.
After the first leg goals extravaganza, this was certainly the most eagerly-awaited second leg of the Round of 16, but could it live up to its pre-match billing?
The game opened as the previous one had closed – with both goalkeepers involved inside the first minute.
But the hosts quickly assumed command and should have gone ahead after five minutes when Kylian Mbappe raced clear only to be denied by a good Caballero save.
Within two minutes, however, Monaco had their lead as Benjamin Mendy jinked his way into the box and, with plenty of time to pick his pass, he played it across goal for Mbappe to score from close range.
It was just the start the Blues hadn’t wanted, but more worryingly, the hosts had their tails up and looked menacing every time they went forward, while City’s attacks were continually crowded out by a packed Monaco midfield.
FORWARD MARCH: Pep Guardiola looks to urge City on
The Blues task became harder still just before the half-hour mark as Monaco again raided down the left flank with the dangerous Mendy who fired a pin-point cross for Fabinho to drill home from 10 yards.
With no shots on target and not so much as a sniff of a threat, City went in at the break with their Champions League destiny hanging by a thread.
The Blues came out for the second half and finally started to look more like the team that had slugged it out with Monaco in the first leg.
After dominating the early passages of play, Kevin De Bruyne threaded a ball through to Raheem Sterling but, faced with the keeper at an angle, he tried to set up the hard-working Sergio Aguero and the danger was cleared.
Minutes later David Silva was sent clear by Fernandinho and after holding the ball up, he played in Aguero who was denied by Subasic – surely the vital away goal had to come before long?
Then Leroy Sane waltzed into the box but went for goal instead of squaring the pass to Aguero and the chance again went begging.
Finally, City’s dominance was rewarded as Sane again broke clear and this time he made no mistake, thumping the ball high into the roof of the net after a Sbasic parry.
JOY: Leroy Sane’s strike put City back in front overall on aggregate
But the elation lasted less than five minutes as Monaco, who had rarely ventured out of their half after the break, regained their crucial two-goal advantage as Bakayoko headed firmly past Caballero from a free-kick and crucially, the hosts were back in the box-seat.
Suddenly Monaco, who had looked dead on their feet, found their second wind and the tie again started to ebb away from the Blues.
Matchday App Star Man: Fernandinho
What it means…
The Blues will now need to focus on securing a top four place with this season’s European adventure over.
CROWDED HOUSE: Sergio Aguero tries to find a way through the Monaco defence
City will aim to collect as many points as possible between now and the end of the campaign as well as trying to win the FA Cup.
What’s next?
The games don’t get any easier with Liverpool next up for Guardiola’s men on Sunday afternoon.
Though the Merseysiders have been spluttering along for the past few months, they know a win will take them above the Blues into third spot at least.
The Reds are unbeaten against teams in the top six this season so this would be the perfect time to put a dent in that record and move four points clear with a game in hand.
