Manchester City F.C. needed a late Samir Nasri goal to snatch a draw with the bottom-placed Black Cats, a result that left them third in the table on 71 points after 33 games, six behind leaders Liverpool who have played 34 matches.
Second-placed Chelsea are on 75 points from 34 games and travel to Anfield on April 27 for a clash that is likely to determine the destination of the title.
"Of course, Manchester City F.C.'s chances are now less. Three points was very important for us ... but we will continue fighting," Pellegrini told the club's website (www.mcfc.com).
"We have five games more in which to play. My duty is now to talk to the players and to win the last five games.
"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. have five games more to play and we will continue to have chances ... this team was six points behind the leaders two years ago and won the title."
Pellegrini's side were lucky to have salvaged just the one point from the game after Connor Wickham scored twice in the second half to give Gus Poyet's side some hope of retaining their position in the top flight.
Nasri, however, gave them a sniff of chasing down Liverpool and Chelsea when Sunderland goalkeeper Vito Mannone fumbled his shot into his own net.
Pellegrini said he had been concerned about facing Sunderland so soon after they lost 3-2 to Liverpool on Sunday at an emotionally charged Anfield, where before the game the Merseyside club commemorated the 25th anniversary of the Hillsborough disaster when 96 supporters were killed.
"Before the match I was worried about this game," the Chilean said about the clash with Sunderland. "Playing against a team fighting relegation is very difficult and we had only four days to get over the Liverpool game.
"My players are more mentally tired than physically tired. Playing this game after Liverpool was very difficult."
Pellegrini's team next face 16th-placed West Bromwich Albion, who are also desperately trying to stave off relegation as they sit on 33 points, three ahead of the 18th-placed Fulham, next Monday.
The remainder of their run into the season finale includes matches against mid-table clubs Crystal Palace (40) and West Ham United (37) and 14th-placed Aston Villa (34), who also face a nervous end to their season and could be desperate for points by their May 7 clash.
The trickiest match for Manchester City F.C., however, looms in the form of Champions League-chasing Everton on May 3 at Goodison Park, especially after Roberto Martinez's side were upset 3-2 by Palace on Wednesday.
That result left Everton in fifth place on 66 points, one behind Arsenal F.C. for the final place in the lucrative Champions League competition next season.