The Romanian produced key saves throughout the game against Newcastle United, effectively keeping them in the tie until two late goals from Edin Dzeko and Alvaro Negredo saw them through to face Leicester City in the next round.
The Chilean has been increasingly frustrated by Hart after a number of high-profile errors and assured Pantilimon that a good enough game against the Magpies would see him given the chance to keep his place.
And Pellegrini told reporters after the match on Wednesday: "I think Costel is a very good goalkeeper. Also, he normally plays in the Capital One Cup and FA Cup, so it is possibly [an] important match for him.
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"[I am] very pleased because it was a very close match, a very difficult match, as Newcastle played very well. Playing 120 minutes is not easy, so it was important to get a result."
Asked if progress into the quarter-finals had him thinking of Wembley, the Chilean replied: "No, absolutely not. If Leicester are there then they deserve to be there. They won two matches before. It is not a team from the Premier League and it won't be an easy match.
"We will have to continue in the Capital One Cup playing the way we played today and see if we can get to the semi-final."
Stevan Jovetic went off injured inside the first five minutes and Pellegrini explained: "[He] has pulled his calf. He was on for five minutes and it was his third injury, so we will see [on Thursday] with the doctor to see what kind of injury [it is]."
The City boss also reflected on Uefa's decision to order a partial stadium closure for CSKA Moscow after a section of their fans racially abused Yaya Toure.
"It is very important that Uefa sanction CSKA about what happened in the stadium because it's the country where the next World Cup will be played," he said. "It's important they find a way to finish all these things.
"I don't know about the severity, whether it should be less or more severe, but Uefa have levels of sanctions and this is the first time."