Manager Pep Guardiola named an attacking line-up for the second leg of the last-16 tie but that backfired as Monaco overturned a 5-3 deficit to win on away goals after a 6-6 aggregate draw.
First-half goals from Kylian Mbappe and Fabinho put the Ligue 1 leaders ahead and although Leroy Sane hit back for City, Tiemoue Bakayoko sealed victory with a header 13 minutes from time.
City were lacklustre on the night and Monaco made light of the absence of Radamel Falcao, scorer of two goals in the pulsating first leg, with a hip injury.
Guardiola, pictured, perhaps got his selection wrong by naming the in-form Yaya Toure on the bench. With Fernandinho the only specialist central midfielder on the field, City were unable to make any impression in that area and Monaco came at them in waves.
That early pressure was quickly rewarded as Mbappe, who had already forced Willy Caballero to make one save, opened the scoring in the eighth minute. City’s defence was cut open as Benjamin Mendy drove in a ball from the left and Mbappe turned in with ruthless efficiency.
Mbappe thought he had claimed a second soon after but his powerful low strike was ruled out for offside.
City struggled to gain possession, made little use of the ball they did get and failed to repel Monaco’s continual raids.
It came as no surprise when they struck again to level the tie just before the half-hour mark. Mbappe again cut the defence open on the left before Mendy crossed and Fabinho made no mistake with a first-time finish.
City’s attacks were few and far between and those they did piece together fizzled out before they reached the box.
It was not until the second half that they started to assert themselves in any way and finally get the previously isolated Sergio Aguero into the game.
Seemingly out of nowhere, a hat-trick of chances came the Argentinian’s way in quick succession but he was unable to take any of them.
He could not be blamed for the first as Andrea Raggi produced a superb challenge to pinch the ball from his toes as he lined up a shot from Raheem Sterling’s pull-back. But the striker blazed over moments later following a lightning break by Sane and he was denied by a fine save from Danijel Subasic after a smart turn by David Silva.
It did seem, however, that the tide had turned and Monaco were maybe starting to feel the pace after such a high-energy start.
Sane took advantage to put City back ahead on aggregate when he pounced from close range after Subasic palmed out a shot from Sterling with 71 minutes gone. Yet that good work was quickly undone when poor set-piece marking allowed Bakayoko to thump home a header from a Thomas Lemar free-kick. City’s hopes drained away and the Stade Louis II, a venue not renowned for its atmosphere, was rocking as the final whistle sounded.