The score on the night was 2-1, Messi and Daniel Alves scoring the Barcelona goals.
Trailing 2-0 from the first leg, City’s best early chance fell to Samir Nasri whose shot was saved by Victor Valdes in the Barca net.
It was goalless at the break and Messi opened the scoring midway through the second half with a cool finish, latching onto a Cesc Fabregas pass after Joleon Lescott gifted possession away.
Joe Hart impressed in the City goal and made a string of saves, while Pablo Zambleta saw red for protesting against a decision not to award his side a penalty kick.
The 10-men managed to equalise in the 89th minute through Vincent Kompany but moments later Barcelona made the extra man count and Alves popped up to score, much like he did in the first leg.
It has been a bad week for City who crashed out of the FA Cup on Sunday after defeat to bogey side Wigan and they face an anxious wait on the extent of an injury to Sergio Aguero who went off at half time.
City have just the Premier League title left to play for but find themselves nine points behind leaders Chelsea with three games in hand.
Wednesday’s other game saw a weakened PSG cruise past Bayern Leverkusen, winning 2-1 on the night and 6-1 on aggregate – Marquinhos and Lavezzi on target after Leverkusen took an early lead.
The French champions remain unbeaten at home in European competition since 2006.
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