It could have worked out differently had Palace been given a penalty inside the first 30 seconds when Santiago Vergini felled Fraizer Campbell in the box.
Fletcher admitted his side had been handed the luck on this occasion.
"The gaffer tells us not to tackle in the box and we got away with one," Fletcher said. "We deserve a bit of luck.
"It was a massive game, three points and the performance of the back four was fantastic. We know we have a good team and we don't listen to outside things."
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