Pellegrini claimed the approach of Palace had blunted his side's normally free-flowing attack.
He said: "I don't think we were fortunate to win the game today.
"Just one team wanted to play the 90 minutes and the other wanted to stay in their own goal.
"I was absolutely sure before it would be a very difficult game.
"It is impossible to play 44 hours after the tough game we played against Liverpool and I knew our team was not fresh so it would be a very difficult game.
"That's why it is so important to know how to win 1-0."
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