Fernandinho gave City the lead inside two minutes at the Etihad Stadium on Wednesday, before Connor Wickham threatened to completely to derail City's title hopes by scoring two goals in 10 second-half minutes.
However, Samir Nasri's late drive was fumbled into the net by Sunderland goalkeeper Vito Mannone, leaving City six points adrift of leaders Liverpool, albeit with a game in hand.
Pellegrini, however, is refusing to concede the title.
"My duty now is to talk to the players and try to win the last five games," he said. "At the end of the season we will see which team has more points.
"Remember, this team two years ago were six points behind the leaders and they won the title at the end, so I think it's difficult, but it's not the last game that we must play today.
"(We have) less chances than before this game, but we continue having chances."
David Silva was left out of the squad on Wednesday, and Pellegrini revealed that the Spaniard had been suffering with an injury.
"David Silva has a problem in his ankle," he added. "He played the last two games in that condition but that was a game each week.
"Playing after three days he couldn't do it today. We'll see how he is for Monday (at home against West Brom). I hope he can play."
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