Going in 2-0 down at half-time, following strikes from Matias Fernandez and Ricky van Wolfswinkel, City repsonded in the second half with two golas from Sergio Aguero, as well as a penalty from Mario Balotelli. Despite late drama, the Premier League side were denied the comeback victory as Sporting held on to progress to the quarter-finals.
Other than the center-back pairing of Kolo Toure and Stefan Savic, City fielded arguably their strongest lineup, suggesting that the Citizens would come out firing in an effort to turn around their 1-0 deficit from the first leg in Lisbon last week.
But Sporting would have been shocked at the ease at which they were able to saunter into a 2-0 lead before half-time.
Sporting's opener arrived in the 33rd minute, via a free kick needlessly conceded by Mario Balotelli just outside the penalty area. Up stepped Chilean Mattias Fernandez, who curled a wonderful strike into the far side of the net.
And the side, currently fourth in Portugal's Liga, doubled their lead five minutes before the break through their top scorer Ricky van Wolfswinkel. Russian Marat Izmailov swept a dangerous ball across the City box and the Dutch striker was on hand to finish from close range at the far post.
This latest setback left the home side needing a virtual miracle, with four goals now required without reply for City to progress.
The home side gave themselves hope on the hour mark. Yaya Toure playing the ball into the box for Aguero, who turned his man with ease before dispatching a quick-fire shot past Rui Patricio.
City finally began to take a grip on the contest and, though they were still not at their best, they were able to get another goal back from the penalty spot. Aguero dove theatrically, and somewhat prematurely, over the challenge of substitute Renato Neto in the box and, despite Sporting's protests, the referee pointed to the spot.
Balotelli strolled forward with his familiar stutter-stepped run up and coolly side-footed the ball to Rui Patricio's right as the keeper stood motionless.
And things got even more interesting when City leveled up the aggregate score with eight minutes remaining. Aguero was once again the scorer as he finished well from point-blank range after Edin Dzeko's flick-on from a corner found the Argentinian at the back post.
With the score now 3-3 on aggregate. City now needed to score once more as a result of the away-goals rule. And they were oh so close to getting a winner. Incredibly, goalkeeper Joe Hart, having abandoned his position between the sticks, found himself on the end of Nigel de Jong's cross. But the fairytale ending was thwarted by a tipped save from Hart's opposite number Rui Patricio.
Despite the drama late-on, Roberto Mancini's men only have themselves to blame for their exit after such a poor opening 45 minutes that left them too much of hole from which to extricate themselves
Both Manchester clubs now have no distractions in their quests to claim the Premier League title.