Barcelona were 2-1 winners in the opening leg of the last-16 tie at Etihad Stadium on Tuesday but it could have been much worse for City after conceding a last-gasp penalty.
Lionel Messi was upended by Pablo Zabaleta in the penalty area but he was unable to extend Barca's lead as Hart dived to his left to keep out the spot-kick before the Argentina star headed the rebound wide.
Hart's late heroics in Manchester could yet be crucial heading into the second leg at Camp Nou on March 18.
"It was a very important save. It was an unnecessary penalty. Of course it gives us more chance to try and win in Barcelona but 3-1 would have been a very difficult score to try and overturn," Pellegrini said afterwards.
"It is not the best result here at home. We are going to play in Barcelona and we will try and do it the way we normally play.
"We have a chance. We must try to do it there in the next game."
City will make the trip to Barcelona in the similar position to last season, when the Catalan giants left Manchester with a 2-0 cushion from the first leg.
Pellegrini's men produced a gallant performance in the return fixture, beaten 2-1 away from home but the Chilean boss is not thinking about what happened last season.
"There is hope and we must support that hope by playing the way we normally do and did in the second half," he said.
"If we don't play to our strengths, it is not easy for our team to win."
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