Goals from David Silva and Fernandinho had put City on course for a club-record 10th consecutive win in all competitions that would have closed the gap to Premier League leaders Chelsea to one point.
However, George Boyd pulled one back shortly after the break at the Etihad Stadium on Sunday, seemingly from an offside position, before Ashley Barnes fired home a loose ball inside the area late on.
Despite failing to take advantage of Chelsea's draw with Southampton earlier in the day, Pellegrini remained upbeat after getting to the halfway point of the league season.
"Football has a lot of things that decide the score, maybe we play well in the first half but after that Burnley score, in a clear offside, a goal and after a rebound the second one," he explained.
"I'm not saying that we are unfortunate, I don't say that. I say the scores in football - in just two balls can decide the score.
"I think we play very well in the first half, in the second half after they scored the goal maybe they grew and we couldn't keep the goal advantage.
"They are a brave team who are always going forward and they score a second goal.
"It's clear we couldn't keep the same intensity in the second half, it was clear because the first goal was very important for them because they grew a lot and have a lot of trust in what they do.
"In the second way, it is difficult for all teams, especially this team, to play on a heavy surface last time [against West Brom on Boxing Day], and keep the same pace in the second half."
Pellegrini was without the injured Sergio Aguero and Edin Dzeko, with Vincent Kompany not risked following a hamstring problem and Yaya Toure rested.
However, the Chilean backed his side to reel in Chelsea during 2015 and dismissed claims it was a case of two points dropped for his side.
"Of course it's a chance to have two points more but we finished the first round with 43 points - a good amount," he added.
"Just because you play at home you shouldn't be sure you are going to get the points.
"I think we have all the second round [to play] and we will be the best team."
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