The defeat kept City nine points behind leaders Chelsea and seemingly now in a battle to finish above Arsenal and Manchester United.
Chelsea, who have eight matches to play, have 70 points, followed by Arsenal on 63, Manchester United on 62 and City on 61. That trio all have seven matches remaining.
Impressive Palace defended resolutely to withstand early City pressure before taking the lead through Glenn Murray after 34 minutes.
He swept in from close range after Scott Dann's shot bounced off goalkeeper Joe Hart's leg into his path.
The goal stood despite City claiming Palace had been offside in the build-up, but there was no argument about Palace's second three minutes into the second half.
Fernandinho brought down the outstanding Murray 20 metres from goal and Jason Puncheon swept his curling free kick over the wall and past Hart into the corner of the goal.
Yaya Toure gave City some hope with a thunderous drive after 78 minutes but although Palace dealt his team what could be a fatal blow to their title hopes, Pellegrini was not conceding the race was over yet.
"We lost to an offside goal and a beautiful free kick and we did not take our chances," he told Sky Sports.
"We are not talking about the title now, or Chelsea. We are just trying to win our games. We have seven games left they are all very important, there are 21 points and all we must do is win our games."
City came to Palace after a run of patchy form with only four wins in their last 13 matches in all competitions and were almost dealt an early blow in the second minute when Wilfried Zaha blasted his angled drive over.
City soon settled with David Silva and Sergio Aguero combining well up front, and Aguero came close to opening the scoring after 19 minutes but saw his shot cannon away off the foot of Julian Speroni's right-hand post.
The match also had echoes of Liverpool's visit to Selhurst Park 11 months ago when they were leading 3-0 with 11 minutes to play, only for Palace to end their title hopes by drawing 3-3.
Palace manager Alan Pardew told Sky: "We showed diligence, character and resilience tonight. We had two quality moments for the goals -- it was a shame we did not have more offensive moments tonight, but we will have other games when that happens."
(Reporting by Mike Collett; editing by Justin Palmer)
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