The Premier League giants gave a spirited display but were undone by the Argentine superstar and Dani Alves late on, with a red card for Pablo Zabaleta compounding their misery
Gerardo Martino, who had been under pressure going into the tie, made two changes to the Barca side beaten by Real Valladolid on Saturday, with Jordi Alba and Andres Iniesta replacing Adriano and Pedro.
Joleon Lescott, Yaya Toure, Samir Nasri and Sergio Aguero were the only City players to retain their starting places following Sunday's shock FA Cup defeat to Wigan, with Pellegrini electing to the ring the changes.
City was aggrieved with a penalty awarded to Messi in the first leg, though it got lucky when the Argentina forward appeared to be caught by Lescott just eight minutes in but referee Syephane Lannoy saw nothing untoward.
The Premier League side was fortunate once again 17 minutes in, when Neymar had the ball in the back of the net, but marauding full back Alba was adjudged to be offside in the build-up, despite appearing to have timed his run to perfection.
The Brazil forward then fired into the side-netting before Joe Hart denied Xavi and Nasri spurned City's best chance of the first half when he shot straight at Victor Valdes from inside the penalty area after a fine move.
City was indebted to Fernandinho a minute before the break when he headed Neymar's shot off the line to ensure that the first half ended goalless.
Aguero was withdrawn at the break due to a hamstring injury and his replacement, Dzeko, took just a minute to test Valdes with a right-foot strike.
Lescott breathed a sigh of relief when he gave the ball away and Messi ended a trademark run with a measured left-foot shot that struck the post five minutes after the break.
City needed a minor miracle, but it looked far more threatening in the opening stages of the second half. Valdes producing an outstanding reflex save to keep out a Dzeko header that looked destined for the top corner of the net.
Zabaleta then sliced a left-footed shot just wide as City began to push forward in search of the goals it needed.
Messi finally eased Barca's nerves after 66 minutes though, coolly finishing with the outside of his left foot after Lescott had clumsily failed to deal with Fabregas' attempted through ball. It was the Argentine's 28th goal of the season and eighth in the current Champions League camapign.
City ought to have had a spot-kick 12 minutes from time when Pique brought down Dzeko, but the French official waved play on and then sent off Zabaleta for his furious protests.
Kompany did give the traveling support something to shout about when he turned in from close range a minute from time, tucking in Dzeko's knockdown.
But Alves had the final say, just as he did in the first leg, as he calmly slotted home a minute into stoppage time after good work from Iniesta to seal victory on the night and ensure Barcelona progressed to the quarterfinals in style.