Glenn Murray's 34th-minute opened preceded Jason Puncheon's fine free-kick on 48 minutes as the Eagles made the most of their opportunities to down the reigning champions who hit back just over 10 minutes from time through Yaya Toure.
Pellegrini claims there should have been an offside call in the lead-up to Murray's opener while ruing his City side's inability to finish the chances they created in south London.
"From the beginning to the end, we had a lot of possession and a lot of chances," he told the club's official website.
"We lost the game because they scored a goal which was clearly offside and then scored again with a beautiful free-kick - that was all they did in the game.
"The beginning of the play [for the first goal] is offside. I don't know if the player who scored was offside - maybe he is behind the ball, I'm not sure.
"I don't want to use excuses about the referee. It is someone else's job to analyse the referee. It is not the managers' duty.
"We were very unlucky not to score more goals but I am very pleased in the way my team played. We missed a lot of chances to score - that was the reason we lost this game."
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