Manchester City F.C. took the lead through Fernandinho's early strike but they struggled to hit top gear and Connor Wickham scored a quick double to put Gus Poyet's men in front.
With time running out, French midfielder Samir Nasri was on hand to spare Manchester City F.C's blushes as his strike squirmed past Victor Mannone two minutes from time to salvage a draw.
"Of course, our chances (of winning the league) are now less," Pellegrini told reporters.
"Three points was very important for us tonight, but we will continue fighting.
"We have five games more in which to play. Liverpool has a better chance than us (of winning the league) and Chelsea but we will continue fighting until the end."
Manchester City F.C. suffered a morale-sapping 3-2 defeat by leaders Liverpool on Sunday and Pellegrini felt victory over Sunderland was a tall order just three days later.
"Before the match I was worried about this game," the Chilean added.
"Playing against a team fighting relegation is very difficult and we had only three days to get over the Liverpool game.
"My players are more mentally tired than physically tired. Playing this game after Liverpool was very difficult."
Manchester City F.C's remaining five games are against West Bromwich Albion, Crystal Palace, Everton, Aston Villa and West Ham United.
Despite trailing Liverpool by six points, the former Real Madrid boss believes City can snatch the title if they show the same spirit they produced when they won it in 2012 after Sergio Aguero scored a late winner in the last game of the season against Queens Park Rangers.
"We have five games more to play and we will continue to have chances," Pellegrini said.
"My duty is now to talk to the players and to win the last five games. This team was six points behind the leaders two years ago and won the title."
A point for Sunderland was not enough to take them off the bottom of the table and Mannone's mistake denied them a crucial victory.
But Poyet defended his goalkeeper, with Sunderland on 26 points from 33 matches and six points adrift of 17th-placed Norwich City.
"It's difficult for Vito," said Poyet. "He has been outstanding for us, but we need to be realistic we were up against a top team and they have some dangerous players on the pitch.
"When we celebrate the victories we celebrate together and then when something doesn't go our way we suffer together."