The hosts took the lead within two minutes at the Etihad Stadium but were nearly undone by a Connor Wickham double before Vito Mannone's late mistake allowed Samir Nasri to equalise.
Pellegrini confessed after the game that he had been "very worried" in anticipation of the game, which ended with his side six points behind the Reds with only one game left in hand, their hopes of winning the title slipping away.
"Chances [of winning the league] are less than before the match," he told the press, "[but] we will continue fighting to the end.
"I don't think there was less confidence. We couldn't take out of our mind the game against Liverpool.
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Attacking midfielder David Silva was a late withdrawal due to an ankle injury but Pellegrini says that the problem is a minor one.
"David has a problem in his ankle," the Chilean stated. "He played the last two games but playing twice in a week wasn’t possible. We will see how he is for Monday."
Sunderland manager Gus Poyet was glad to have got some reward for his side's efforts, though he remains cautious on their chances of survival, with the Black Cats still six points from safety with only one game in hand.
He remarked: "I'm realistic and I'm not going to change now. We played a great game and we deserved something.
"You need to realise the situation we are in and I think all of you [the media] thought we would collapse. The players know how important it is to the club and fans and the need to keep going.
"It's going to give us a little bit of confidence and give us a chance to go with a different two approaches for the rest of the season.
"I'm sure the players will go there [to Chelsea] and play. We are not playing for Liverpool. I'm sure Luis Suarez is going to be happy tonight, with one team less [in the title race]."
Wickham, who scored both Sunderland goals, had only recently returned from a loan spell at Leeds United but Poyet declared his faith in the youngster.
"When I got to the club there were five or six strikers. It was impossible to play them all," the Uruguayan recalled. "He went away and played well.
"If he delivers, he's going to keep playing. It's very simple in our situation. If you deliver, then you will get the chance to play."