Roberto Mancini's side pay for a sluggish start at home as they fall astonishingly short of scoring four goals required to progress to the last 16 of the Europa League
First half goals from Matias Fernandez and Ricky Van Wolfswinkel gave Sporting a deserved 2-0 lead as City started sluggishly to leave them with the tough task of scoring four goals in the second half.
But Roberto Mancini rung the changes and his team got back into the game through two goals from Sergio Aguero either side of a Mario Balotelli penalty.
Aguero’s goal gave the home side’s fans hope with the third goal nine minutes from time but despite throwing everything at Sporting, they couldn’t find the fourth.
Midfielder David Pizarro was given a rare start after Gareth Barry failed to recover from a back injury in time, while Joleon Lescott missed out again.
Aguero started alongside Balotelli in City's quest for goals and Alexandre Xandao, who scored Sporting's back-heeled goal in the first-leg, started for the away side.
Sporting made the brighter start to the game and Xandao went close with a header in the opening stages but a low-key start from both teams was indicative of the atmosphere at the Etihad Stadium, which was barely full despite the importance of the game.
The away side were denied a penalty claim after Fernandez fell under the challenge of the clumsy Stefan Savic. Unimpressed with his histrionics, the referee booked the midfielder five minutes later for diving just outside the area - although Pizarro did appear to catch his compatriot
City seemed bereft of rhythm in the first half as they looked for long balls, while the effervescent Fernandez kept the away side ticking.
And it was Fernandez who opened the scoring with a fabulous free kick from 25 yards. The Chilean went down under the challenge of Balotelli and stepped up with to fire an effort into the far corner that had too much power on it for the diving Joe Hart to keep out, despite getting a strong hand on it.
Sporting deservedly extended their lead less than ten minutes later with a brilliant team goal. A cross field ball was headed down by Van Wolfswinkel who spread the ball wide to Marat Izmailov who expertly found the Dutchman at the back post and the former Utrecht man swept home to seemingly kill the tie.
Despite his team being desperate for goals in the second half, Roberto Mancini brought off Adam Johnson, who had showed a few bright spots in the first half, for holding midfielder Nigel de Jong and bringing on Edin Dzeko for Pizarro.
City got themselves back in the game on the hour mark with their most fluent piece play of the game as Yaya Toure drove towards the area with the ball before expertly finding Aguero who did well to finish in the top corner.
The goal brought City to life and they immediately took control of proceedings as Sporting began to look nervous and tried to protect their lead.
City’s pressure told 15 minutes later as Aguero was tripped by Renato Neto and Balotelli who had been virtually absent for the whole evening stepped up to draw the teams level on the night.
Aguero then sent the home fans into raptures with just under 10 minutes to go. A corner was flicked on by Dzeko towards the Argentine, who was all alone at the back, to smash the ball home.
City had one last chance as JOe Hart went up for a corner and saw a header tipped away by Patricio but they could not grab a winner and crashed out of the Europa League along with Premier League title rivals Manchester United.