In another clash overshadowed by refereeing controversy, City had Pablo Zabaleta sent off as they were beaten 2-1 in the Nou Camp to go out 4-1 on aggregate at the last-16 stage.
City captain Vincent Kompany did briefly level the scores at 1-1 in the closing minutes but it proved mere consolation.
For a spell when the score was still 0-0, particularly early in the second half, City troubled the Spanish champions but could not find the goal that would change the tie.
Samir Nasri had a good chance in the first half while substitute Edin Dzeko brought a good save out of Victor Valdes with a header after coming on at the interval.
But, in truth, Barca should have been in the lead long before Messi finally struck with a neat dink, after pouncing on a Joleon Lescott error, in the 67th minute.
Lescott had been fortunate not to concede a penalty after felling Messi early in the match and City also breathed again when a Neymar goal was harshly disallowed for offside.
City were on the wrong end of a decision from referee Stephane Lannoy themselves when Dzeko was denied a penalty after being clipped by Gerard Pique.
Zabaleta was sent off for protesting in the arguments that followed.
The result saw City eliminated from a second competition in the space of three days after Sunday's FA Cup loss to Wigan.
Attention now turns to the Premier League, in which they trail Chelsea by nine points with three games in hand.
Kompany said: "If anything, it should give us motivation.
"The way we played against Wigan, the performance was completely different.
"Only the winners get remembered, but it's only the third year ever for Manchester City in the Champions League.
"I'm looking at this and I don't see why next year we should fear anyone."
Kompany was proud of the efforts of his team-mates.
He said: "I think I speak for the team in saying we've got nothing left in the tank."
Zabaleta was frustrated about his dismissal for a second yellow card.
He said: "It was very clear. I think Pique was behind and made the tackle on Edin Dzeko and the referee was only two metres away from that.
"I don't know why I was sent off. I went to him to talk to him in a good way. I was a little bit angry to him because he didn't give a penalty but I have always been very respectful to him.
"I am frustrated. I think it was a shocking decision."
In further bad news for City, top scorer Sergio Aguero suffered another hamstring problem and will require a scan.
Aguero said: "I felt a twinge in the leg early on after a challenge with Messi.
"I carried on with it for the rest of the half but at half-time we decided not to risk it."
- Sports & Recreation
- Vincent Kompany
- Manchester City
- Pablo Zabaleta
- Edin Dzeko