"There is something about the cup that gets players up for the game," Pardew said.
"It was quite an open game and I can't quite put my finger on it why that would be so, more than in a Premier League game."
But Pardew said his side deserved credit for their performance, with the Eagles maintaining their 100 per cent record under the former Newcastle boss since he took over at Selhurst Park earlier this month.
"Both of their goals were poor goals from our point of view, but to score immediately was important for us and it increased our belief.
"We got ourselves in front and then we had to play a bit differently, because we knew that Southampton would keep coming and coming, but it was a great win for us.
"That is four games now where we have had to show different qualities, but we have shown we can win games."
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