Having won the first-leg 5-3 at the Etihad, City's buoyant mood coming into the return fixture was quickly quashed by a dire first-half performance in which they conceded twice, putting the score at 2-0, a result that would have sent the hosts through on away goals.
Turning things around after the break, Leroy Sané's goal swung the tie back in the Citizens' favour, albeit briefly, with Tiemoue Bakayoko's 77th minute header putting the Ligue 1 side back ahead on the away goals rule, the method by which they would progress as City failed to find a late goal.
No Falcao, no problem?
There was a setback before the game had even started for the hosts as it was confirmed that Radamel Falcao wasn't fit enough to even make the bench, heaping even more pressure on teenage sensation Kylian Mbappé.
The 18-year-old had a chance to open the scoring very early on as his pace got the better of Alexsandar Kolarov running forward, bursting through on goal only for Willy Caballero to produce a stunning stop.
However, City didn't react to that chance, conceding to the same man just seconds later. Failing to clear not once, but twice, from the resulting corner, Bernardo Silva's cross eventually found it's way to Mbappé, who prodded in at the near post.
He had the ball in the net again before City had even managed to mount a meaningful attack, floating offside as the ball was bent through to him, before lashing a shot across goal and into the bottom corner. Fortunately for the Citizens, the flag was raised.
Monaco's ground often struggles to sell-out, but it was a full house that were witnessing their team tear City to shreds in the first-half.
Fabinho finds a second
The second goal was again sourced from the left-wing, Benjamin Mendy unmarked as he overlapped Thomas Lemar, thundering a cross perfectly into the path of the arriving Fabinho, who smashed a first-time finish past Caballero.
Fabinho could have bagged another minutes later, this time for outside the area, only for Fernandinho to bravely charge down his shot.
City continued to toil going forward, not managing a shot in the first-half.
City improve, with Sane netting
Guardiola's half-time team talk seemed to be working as the visitors started the second-half with much more energy, which led to a great chance being ruined by Raheem Sterling.
Played in behind the defence after impressive work from John Stones, Sterling had to pick whether to shoot on his left or cut the ball back to Sergio Aguero. Looking to act based on the opposition, Sterling waited for a Monaco player to move towards him, but nobody did, the winger eventually seeing his pull back to Aguero intercepted by Raggi.
The first shot of the game for Pep Guardiola's men would follow soon after, another golden opportunity going begging. Leroy Sané's pace allowed him to skip past the challenge of Raggi and into the area, finding Aguero with a low cross, only for the Argentine to prod the ball over with the goal at his mercy.
Monaco were suddenly on the back-foot, with nerves felt around the ground. However, Aguero again couldn't capitalise. Fernandinho found Silva with a good ball, before the Spaniard showed excellent awareness in the area to turn and set up the striker, whose first touch got away from him before shooting straight at Danijel Subasic.
Things really weren't going for the Citizens as Sané put one wide after getting one-on-one with Subasic, albeit from a tight angle.
That mood was over quickly, with Sané bagging a crucial goal soon after.
Raheem Sterling deserves credit for his bursting run inside from the right, forcing the 'keeper into action with a low left-footed effort, one pushed away from goal, towards the lightning reactions of Sané, who kept his cool to pop the ball into the empty net.
Bakayoko bags brilliant winner
Unfortunately for City, their led in the tie didn't last for long, Guardiola's men crumbling under the pressure with 13 minutes to go, as Tiemoue Bakayoko put the hosts back in the driving seat.
Thomas Lemar's free-kick from the right hand side was a good one, met by an even better header from Bakayoko, who watched in delight as the ball flew into the bottom right hand corner.
That put Monaco back ahead by virtue of the away goals rule, with the tie an astonishing 6-6 on aggregate.
Guardiola eventually thre Kelechi Iheanacho on, desperate to change things, but a catalyst wasn't found.
After all the missed chances before the relief at Sané's goal, Bakayoko's header left City deflated, unable to muster any kind of opportunity, and eventually out of the Champions League.