The Saints head into the game on the back of a disappointing defeat to Watford after the Hornets left St Mary’s with a 2-0 win on Saturday.
Palace could also have a new manager in place, with Roy Hodgson the favourite to replace Frank de Boer after his sacking on Monday.
While Southampton’s squad are determined to bounce back, Davis insists they cannot get carried away and make sloppy mistakes.
With their task possibly made harder due to De Boer’s sacking, Davis has urged his team to be patient.
He told the club’s official website: “I was a little bit surprised that they’ve made that decision so early on in the season but we’re expecting a tough game.
“I watched the game against Burnley and they were unfortunate not to take something from that. They’ve still got a lot of quality players who can hurt you and Selhurst Park isn’t an easy place to go. The crowd always gets right behind them.
“We’ll be expecting their players, with a new manager potentially coming in, to give their best and try to get themselves out of the position they’re in now.
“It will be a tough game but we’re looking at it from our point of view, and we need to improve from Saturday’s game.
“We know we can do a lot better than that. There’s a lot of anger and disappointment with the way we played but we need to stick together now.”