Goals from Glenn Murray and Jason Puncheon either side of half-time left the reigning champions nine points adrift of leaders Chelsea with seven matches remaining.
But there was more than a hint of offside about Murray's strike, with both the striker and Scott Dann appearing to be beyond the last man, while Murray was also involved in controversy at the other end when the ball hit his arm in the penalty area.
"It was a clear offside
Also it was a clear penalty," said City boss Pellegrini
"But with the way we played we must win this game.
"Its difficult to understand the result, we played a good game from the beginning to the end, we had a lot of chances to score.
"Although the second goal was a beautiful free-kick, it's the only thing I remember near our box, so it's difficult to understand but football happens like this."
Sergio Aguero had already hit a post when Palace took the lead, Dann forcing a save from Joe Hart with Murray tapping in the rebound and City's protests proving to be in vain.
But if there were question marks about the first goal, there was nothing wrong with the second three minutes after the interval.
Murray was barged over 25 yards out and Puncheon stepped up to curl a stunning free-kick over the wall and beyond the despairing dive of Hart.
Yaya Toure's ferocious curler 12 minutes from the end halved the deficit, but City could not find an equaliser to leave Pellegrini's position at the club under more scrutiny.
But he added: "I'm not concerned about my job
That is one thing I am never concerned with.
"I never have fear about it, I do my work, I'm very happy
The team maybe have a difficult season but never worry about me.
"We are not thinking about Chelsea, or about the title
We are just trying to win our games."
By contrast it was another big scalp and a memorable night for Palace, whose revival under manager Alan Pardew shows no sign of letting up.
"It was a huge night for us; the champions under pressure playing at our place," said Pardew
"We didn't see too much of ball early on but our diligence, our character and our resilience saw us home along with two quality moments.
"The first goal was going to be important, to set the mood for the game, and we managed to get it.
"We had some scary moments - I counted about 23 - but we held out
They kept coming at us, they got a great goal and I feared they might take a draw but it was our night.
"We had a couple of breaks tonight - the goal looked offside - but I felt we deserved them."
Source : PA
Source: PA