The 2012 Premier League champions lost 3-2 to leaders Liverpool on Sunday and their title hopes were heavily dented on Wednesday as they drew their first of two games in hand on their rivals.
City made a flying start as Fernandinho broke the deadlock in the second minute, only for a second-half brace from Connor Wickham to hand the advantage to Sunderland.
The hosts snatched a late draw courtesy of a Samir Nasri strike, but Pellegrini believes City's heads were elsewhere.
The stalemate leaves City six shy of Liverpool with just one game in hand and the Chilean coach admitted their performance was lacking.
"There were a lot of things missing from the team today," he told Sky Sports.
"I think the most important thing is we could not take out of our minds the game against Liverpool."
However, despite admitting a draw has done their campaign more harm than good, Pellegrini is not willing to rule City out of the title race yet.
"We are in a worse position but there are still mathematical chances and we will fight to the end," he vowed.
City enjoyed the better start but Pellegrini acknowledged the spirit of Sunderland, claiming teams that are fighting for survival prove to be dangerous at this stage of the season.
"We started very well but as the game continued we started losing the ball too easy and we didn't recover well," he added.
"I always say that playing against relegation teams at the end of the season is very difficult because they fight.
"Sunderland fought a lot and played better than we did at times."
City are back in action on Monday night when they play host to Pepe Mel's West Bromwich Albion at the Etihad Stadium.