Samir Nasri, Edin Džeko and Pablo Zabaleta failed to convert three excellent chances with the scoreline goalless before Lionel Messi clipped the ball past Joe Hart in the 67th minute to effectively kill the tie.
Zabaleta was sent off for remonstrating with error-prone referee Stéphane Lannoy yet City levelled through captain Vincent Kompany late on. Barça swiftly regained their lead through right-back Dani Alves, whose second goal in the first leg was so pivotal, to win the tie 4-1 on aggregate.
Barcelona were wrongly disallowed a goal for offside in the first period and a penalty for the calamitous Joleon Lescott's foul on Messi in a contest which will unfortunately be remembered for some wretched refereeing.
City were the more enterprising side after a goalless first 45 but succumbed to Messi's majesty. Having earlier hit the post, the Argentine made no mistake when he pounced on Lescott's failed attempt to clear a Cesc Fàbregas pass and dinked the ball over Hart.
Džeko charged into the area with Barça a goal ahead and had strong claims for a penalty as he went down under a Gerard Piqué challenge.
City's players were furious nothing was given but Zabaleta took his protests too far and was given his marching orders with a second yellow card.
Kompany pulled one back after Džeko won a header at a corner but it was too little too late and Alves again caught them on the break in the dying moments.