Luis Suarez scored twice in the first half as Barca dominated proceedings at The Etihad, the former Liverpool striker driving home a rebound before adding a second with a neat finish in the 30th minute.
However, City held firm and eventually pulled a goal back in the 69th minute thanks to a brilliant finish from Sergio Aguero.
Manuel Pellegrini’s men were reduced to 10 men when Gael Clichy was shown a second yellow card, before Lionel Messi had a late penalty saved by Hart.
And the England goalkeeper is sure that the Premier League outfit are still in with a chance of reaching the last eight.
Hart told ITV: “I hope so [that the penalty save could prove crucial]. We will go there with a great group of fans, belief and we will have a right go.
“We pressed until the first goal and panicked a bit. We regrouped second half, put a lot of pressure on and were good for our goal and maybe good for a result tonight.
“The occasion did not get to us, sometimes things go against you. It is 2-1 and we go there with belief.”
Manchester City, who are currently five points behind leaders Chelsea in the Premier League, travel to Liverpool on Sunday.
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