The result was a major blow for the champions who are chasing a third title in four seasons but remain second behind Chelsea on 58 points with nine matches to play.
The full repercussions of Saturday's defeat may not be felt until Sunday when Chelsea, who have 63 points and two matches in hand, play Southampton at Stamford Bridge.
"When you have a mathematical chance you have a chance to win the title," Pellegrini told Sky Sports. "The reality is that it's more difficult to do so now."
City were beaten despite having 71 percent possession at Turf Moor and 21 goal attempts compared to Burnley's 29 percent and 10 attempts.
But City's failure to find the net in the league for only the third time this season, and a wayward performance from usually influential midfielder Yaya Toure, swung the points Burnley's way.
The visitors had a strong claim for a penalty denied by referee Andre Marriner when Pablo Zabaleta appeared to be felled by Ben Mee late in the game while Sergio Aguero wasted a golden chance with a header with time running out.
Even the introduction of Frank Lampard, for his 600th Premier League appearance late in the game, only Ryan Giggs has played more, Wilfried Bony and Stefan Jovetic failed to turn the match away from the home side who had not beaten City in 13 league or cup matches since October 1974.
Recent media reports have suggested that all is not well in City's camp with allegations of a training ground bustup, and Pellegrini did admit there were problems.
"Of course we're doing something wrong as we are not winning the games we normally do" he said.
Two defeats in their last three league games proves his point and if they are to retain any hopes of another title they need to rediscover their form quickly and hope Chelsea lose theirs.
(Editing by Tony Jimenez)
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