"We are in a worse position but there are still mathematical chances and we will fight to the end," he told Sky Sports News.
"We started very well but as the game continued we started losing the ball too easy and we didn't recover well.
"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."
Pellegrini also admitted that his players were still sore from last weekend's 3-2 defeat to Liverpool at Anfield.