The reigning Premier League champions dominated the opening exchanges at Selhurst Park, but were dealt a sucker punch in the 34rd minute when Glenn Murray tapped home from close range.
City felt the goal should not have stood, claiming that both Murray and Scott Dann were offside in the build-up, with replays showing the two decisions to be marginal.
But the effort was allowed to stand, and Jason Puncheon's free-kick early in the second half rubbed salt into City's wounds, with Yaya Toure's fine strike with 12 minutes to go counting for little.
City are now nine points behind league leaders Chelsea, having played a game more.
"We played a good game from beginning to end, had a lot of chances, and we lost the game because they scored an offside goal and a beautiful free-kick," Pellegrini told Sky Sports.
"I don't want to have this discussion about the referee, it's not a good duty of the manager to analyse the referee.
"You asked me why we lost and I repeat, because of an offside goal and a beautiful free-kick."
When quizzed about City's faint hopes of retaining their title, Pellegrini insisted his team will continue to play game-by-game.
"I'm not talking about the title, I'm just trying to win our games and we will see at the end of the season," he added.
"Every time you drop points it is a big blow but we must try to play in the way we did today because normally we win the game.
"We're just thinking about what we can do in trying to win our games and see at the end of the season which position we are in."
