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City needed to win the first of their two games in hand on Liverpool to keep the pressure on the league leaders and second-placed Chelsea.
But Wednesday's draw with Sunderland, in which they needed a late equaliser from Samir Nasri just to avoid defeat, means that they are still six points behind Liverpool with just one extra game to play.
Pellegrini hopes that wins in City's five remaining fixtures will still give them a chance, but he admitted that his team had been unable to recover from the mental strain of losing 3-2 at Anfield last weekend.
"Of course our chances are less than before the match," he said.
"It was very important for us to win this match
We could not, but we will continue fighting until the end.
"I don't think we could take out of our minds the game against Liverpool
That's why the team did not play well today (Wednesday).
"It was difficult for the players to get Liverpool out of their minds
We needed more intensity, but maybe it wasn't in their minds to do it.
"They were mentally tired
It was difficult to play this game after Liverpool.
"Before the match I was very worried, because when you play against a team that might be relegated at the end of the season, they come and fight for every ball like it's the last."
The injury suffered by Yaya Toure at Liverpool also had an impact as his absence was clearly felt in City's midfield, along with that of David Silva.
Silva was ruled out with an ankle problem, but Pellegrini hopes the playmaker will be fit to face West Bromwich Albion next Monday.
- 'Suarez will be happy' -
And despite this setback, which looked like being a defeat after Connor Wickham scored twice to put Sunderland ahead, the Chilean is not writing off City's chances of an unlikely title success
He added: "There are five more games to play and we must try and win them and see where that takes us at the end of the season, and which team has the most points.
"Maybe Liverpool and Chelsea have a better chance than our team, but we will continue fighting until the last game
It's difficult, but this wasn't the last game played today."
Sunderland's concerns are at the other end of the table and despite a heroic effort, they are now without a win in 10 games.
Goalkeeper Vito Mannone's late fumble of Nasri's shot cost them dear, but manager Gus Poyet was delighted by his players, who hit back through Wickham's brace after Fernandinho had given City a 2nd-minute lead.
"We played a great game and deserved something
I thought for a few minutes it was going to be all three points," said Poyet.
"The situation we are in, bottom of the table and we concede a goal after two minutes
Everyone would have expected us to collapse, but we didn't.
"The players showed how important it is, for the club and the fans, to go to the end, whatever the result is.
"I am proud of the players
They kept going and it was not easy
It's going to give us a bit more of that word I hate -- confidence -- and will give us a different approach on Saturday (at Chelsea)."
The result did little to help Sunderland's plight at the foot of the table as they remain six points away from safety.
But Poyet admitted that his fellow Uruguayan, Liverpool striker Luiz Suarez, will have been delighted by the outcome.
He added: "We were playing for ourselves, not for Liverpool, although we have helped them for sure and Mr Suarez will be happy tonight."
Source: AFP