It was thanks to Hart's heroics that Barcelona could manage only a 1-0 win at the Nou Camp.
Ivan Rakitic scored the only goal of another one-sided encounter between the two sides, completing a 3-1 aggregate win to secure the Catalan giants' place in the quarter-finals.
City did show some spirit in the second half, and could have pulled one back when Sergio Aguero had a penalty saved by Marc-Andre ter Stegen, but in truth the scoreline flattered them.
Barcelona were in a different league to the English champions and Messi was simply outstanding.
One of the enduring images from the game will be his first-half nutmeg on James Milner, who was bamboozled and left on the turf by the Argentinian's brilliance.
It said much for City's night that their man of the match was comfortably Hart, who made a strong of brilliant saves in the second half to limit the damage.
The loss will leave City manager Manuel Pellegrini fighting for his future but even the greatest coaches might have struggled against Barcelona in this mood.
CIty's defeat meant the end of English involvement in the Champions League, after Arsenal and Chelsea's defeats at the same last-16 stage and Liverpool's elimination after the group round.
Pellegrini changed tactics, deploying Aguero as a lone striker, but it was to little avail.
After being well beaten in the first leg, it always seemed likely City would follow all their Premier League rivals out of the competition.
And so it proved as Barcelona set about them from the outset, looking in ominous form as Dani Alves forced a Vincent Kompany error and Neymar rolled a shot against the post.
Barcelona were relentless with Messi at his most ingenious best, continually wrong-footing City with masterful control and movement.
Messi combined brilliantly with Andres Iniesta in the box but Hart came to City's rescue with a low save from the Argentinian.
City could not keep pace with the Primera Division leaders and four of their players - Fernandinho, Aleksandar Kolarov, David Silva and Samir Nasri - were booked inside the first 36 minutes
Nasri was actually lucky not to see red for hacking at the ankles of Neymar.
But by then City were already a goal down after Messi picked out Rakitic in space in the box with a brilliant cross.
Rakitic controlled superbly on his chest and reacted quickly to lob the advancing Hart.
City's torture continued as Messi, who had earlier been crudely hacked down on the touchline by Kolarov, reacted with great dexterity as Milner attempted to close him down out wide.
Messi simply flicked the ball back inside, nutmegging the England international and dumping him on his backside
Former Barcelona manager Pep Guardiola, watching in the stands, put his head in his hands in disbelief.
Barcelona almost had a second goal before the break as Luis Suarez, scorer of two in the first leg, broke clear and beat the advancing Hart only for his shot to bounce off the far post.
The one-way traffic continued as Hart saved from Iniesta, Rakitic and Jordi Alba in the opening minutes of the second half.
Pellegrini attempted to change shape, with Jesus Navas having replaced the ineffective Nasri at the interval and by pushing Toure forward, but Barcelona were not greatly troubled despite an increase in City possession.
One good opportunity did open up when Navas got to the byline but there was no-one on hand to turn in his cross.
Barcelona still had the menace to kill the game at any moment and Suarez lashed a shot into the side-netting before Messi skipped a challenge on a lightning counter-attack but was forced wide.
Alba thought he had scored a second when he snaffled a rebound after Hart blocked a Neymar shot but offside was given.
Hart denied Neymar again on the hour and City were given a potential lifeline moments later as they broke up to the other end and Aguero fell as Gerard Pique challenged.
A penalty was awarded but Aguero could not take advantage as Ter Stegen saved to his right.
It was not going to be City's night but Hart could still hold his head high, saving again from Suarez before the former Liverpool star hit the bar.
Hart saved brilliantly again from Messi in the last minute and Neymar was also frustrated by him in injury time.
Source : PA
Source: PA