City go to south London without a win in four games, and defeat would leave them behind relegation favourites Palace after more than half the Premier League season.
But Hughton, who is confident striker Gary Hooper will be fit, took encouragement from his side's performance against Manchester United on Saturday despite the visitors' 1-0 victory.
He said: "I can understand the terminology of a 'six-pointer' and I suppose any game with a team around can be called that.
"But I think with the way the league is at the moment there will be a lot of games that could be called that.
"We are on the back of a very good performance if not result against Manchester United, but we're very conscious of the league position we are in and it's of course a position which we'd prefer not to be in.
"There's always an opportunity, though, and the next one is a game away to Crystal Palace on Wednesday, and we will be endeavouring and giving everything to win the game."
Hooper was substituted at the weekend after complaining of muscle tightness, while Jonny Howson missed out with a back injury.
"At the moment, Hooper's okay," Hughton said. "It was very much a precaution.
"It was something he flagged up to us at half-time and we needed to be sure that he was going to be okay. We expect him to train tomorrow (Tuesday).
"Jonny Howson is a doubt as he has been for the last couple of games, but we're giving him every opportunity to come through."