Hart played on after suffering a cut close to the eye to make a number of crucial saves as City claimed top spot in the Barclays Premier League with a hard-fought 1-0 win at the Etihad Stadium.
A club official later confirmed Hart had needed five stitches after being hurt in a collision with Palace striker Cameron Jerome during the first half.
His man-of-the-match performance in the second half, as Palace grew in confidence, made light of the injury and fully justified his recent recall to the side after being dropped for a spell.
Pellegrini, who had been unaware stitches were needed as he gave his post-match press conference, said: "It was not a serious problem. The doctors said he doesn't have serious problem. There isn't a problem with his sight."
Hart was dropped by Pellegrini at the end of October after a series of high-profile errors for club and country.
Costel Pantilimon took his place for seven Premier League games and Pellegrini believes the break has done Hart good.
He said: "I repeat what I said last week, it was very good for Joe Hart to have a rest.
"He needed a rest and he is playing at his normal performance level, as the good goalkeeper he is.
"He worked very hard but he was always confident he would return to his position."
Pellegrini made six changes for the fixture, which came just two days after the Boxing Day win over Liverpool, and the intensity level appeared to drop.
It took until the 66th minute for Edin Dzeko to break the deadlock against a resilient Palace side who might feel unfortunate not to have claimed a point.
But Pellegrini claimed the approach of Palace had blunted his side's normally free-flowing attack.
He said: "I don't think we were fortunate to win the game today.
"Just one team wanted to play the 90 minutes and the other wanted to stay in their own goal.
"I was absolutely sure before it would be a very difficult game.
"It is impossible to play 44 hours after the tough game we played against Liverpool and I knew our team was not fresh so it would be a very difficult game.
"That's why it is so important to know how to win 1-0."
Palace boss Tony Pulis disagreed with Pellegrini's assessment, believing his side acquitted themselves well.
"Did they give Joe Hart man of the match? There you go," said Pulis, when asked his opinion of Pellegrini's comments.
"We are disappointed. It was always going to be a tough game, playing the second away game in a few days, and coming to Man City who are the form team in the Premier League, it was always going to be a tough ask and a tough challenge.
"The players went about their business very well.
"We looked very solid, the shape was good and we looked dangerous on the break.
"It is just about picking that final pass or finishing off the opportunities."
After pinching a 1-0 win with an injury-time Dwight Gayle strike at Aston Villa, Pulis admitted his side needed to squeeze as many points from close games as they can to avoid the drop.
Pulis said: "We have gone away and done well. What we need to do is turn 1-0 defeats into draws if we can or even victories.
"It will be tight but we are in the group now which is something we weren't when I came.
"If we can bring a few players in and strengthen it up a little bit we can give it a good blast when the year turns round."
Pulis confirmed Jerome suffered an ankle injury in the clash with Hart - which ended his involvement - and will be assessed in the coming days.