The result leaves West Ham above the dropzone by two points with five games to play.
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Carragher said on Sky Sports: "West Ham fans will probably be slighlty disappointed right now but I think it will feel better with every day that passes.
"You are playing against Palace who are in good form, a side who got to bring on (Jean-Philippe) Mateta and (Ismaila) Sarr.
"The two centre-backs were absolutely outstanding. They are going to need that if they are to stay up.
"They have got an away game out of the way, whereas Tottenham had a home game. They are in the same position."