It could have been even worse for City who needed a late equaliser by Samir Nasri to avoid defeat, but Liverpool are now six points ahead having only played a single game more while Chelsea are four points in front.
Sunderland's survival chances remain slim but Connor Wickham's double - his first league goals for Sunderland since October 2011 - after Fernandinho had given City an early lead keeps their hopes alive.
Pellegrini blamed Sunday's defeat at Liverpool for affecting the players. He said: "Of course the chances are less than before the match. It was very important for us to win the three points, for different reasons we couldn't but we continue fighting to the end.
"I think we couldn't take out of the mind the game against Liverpool and that was the consequence why the team didn't play well. We needed more intensity but our mind maybe was not in the moment to do it. Maybe at the moment Liverpool and Chelsea have better chances than our team because we are in third position but we still continue fighting until the last game."
Pellegrini insisted however the players would keep going to the very end of the season - and pointed out they had come from six points behind to win the title in 2012.
"We have to play five games more so we continue having chances, less chances than before this game, but we continue having chances," he added. "Remember this team two years ago were six points behind the leaders and they won the title at the end. So it is difficult - but it is not the last game we play today."
Black Cats fight for survival
Sunderland's boss Gus Poyet admitted his fellow Uruguayan Luis Suarez would be delighted with the result - and the Black Cats now have to face Chelsea away at the weekend. Poyet said: "We got a point and now I'm sure all the players are believing they can get at least that if they play the same way at Chelsea.
"We are playing for ourselves - we are not playing for Liverpool. Maybe we helped them, and I am sure that Luis Suarez is going to be happy tonight because there is one team less."
Poyet did rue City's late equaliser - agonising for Vito Mannone who got a hand to the ball but saw it squirm over the line. Poyet added: "It's one more blow. I tell you what, I'm testing my heart this year. Every week. I'm realistic and I'm not going to change now. We played a great game and took something from it.
"I thought for a few minutes we were going to get all three points, but we didn't because of an incredible moment again.
"I think everyone was expecting us to collapse and concede five or six, but we didn't. "We won't stop or give up because the players know how important it is for the fans and the club to keep going until the end."
Poyet also refused to be drawn on his own future, saying the speculation was just "stupidity". He added: "There has been so much stupidity in the last two days about Sunderland that it's getting unbearable really. Apparently nobody talks about Sunderland apart from when we play against the top teams.
"Then everybody uses this time to talk stupidity and try to imagine things."