The Catalans were unable to breakthrough the Blues defence in the first half but midway through the second period that all changed.
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Dani Alves added a second for Gerardo Martino's men late in the game to leave Manuel Pellegrini's side needing a minor miracle at Camp Nou to reach the quarter-finals.
"It is a terrific result for us," Iniesta, 29, told reporters. "They tightened up their defence a lot, even with a man down, but we knew if we had the ball a lot then we would score a goal.
"City have players of a very high level, this required a performance like that. A lot of possession and chances eventually materialise.
"It is a very good result but we cannot be over confident."
Demichelis' red card was a defining moment in the match, with Iniesta expressing there was little doubt in his mind it was a deserved penalty and a sending off.
"The penalty was clear as he was the last defender, so the expulsion is fair too," he added.
History is now against Man City as no team has ever come back from a 2-0 knock-out loss on home turf in a Champions League first leg to go on to qualify for the subsequent round of matches.