Gary Cahill admitted Chelsea’s run of four defeats in five Premier League matches before beating the Eagles had damaged their bid to finish in the top four.
The Blues ran out 2-1 winners against their south London opponents to put themselves just two points off a spot in the Champions League postitions.
Willian’s low shot gave Chelsea the lead after 25 minutes before Martin Kelly’s own goal doubled their advantage.
Antonio Conte’s side missed a catalogue of chances to extend their lead and they were nearly made to pay when Patrick Van Aanholt’s 89th-minute goal made it a nervy ending the game.
However, the Blues held on for the win and Cahill insisted that the team needs to bring the same character they showed against the Eagles for their remaining games.
The centre-back told BT Sport: “We’ve put ourselves in a difficult situation and we have to work hard together to get ourselves out of it.
“Up until the Bournemouth game things were fine and then, as we know, the results haven’t gone our way and we put ourselves in a tough spot.
“We have to show the kind of character and the work-rate we showed today to finish in the top four and that’s certainly our ambition between now and the end of the season.”
The Blues next face Barcelona in their Champions League last-16 second leg game at the Nou Camp, and the Chelsea boss was upbeat ahead of it.
Conte said: “We created a lot of chances to score a lot of goals today. We conceded (to make it) 2-1 at the end and then for sure there is a bit of pressure. But I think we were very, very good to keep the ball outside of our box.
“I think we deserved to win, we played a really good game, especially in the first half then in the second half we created other chances to score against a good Crystal Palace.
“When you have so many chances it’s important to be clinical and to try to finish the game quickly.
“We must be pleased with the performance of the team and now we try to prepare in the right way for the game against Barcelona.”
Defeat for the Eagles sees them remain in the relegation zone and manager Roy Hodgson was left ruing his side’s slow start to the game.
Hodgson said: “I was very disappointed in the first-half. Not the football I know we can play. We were not aggressive enough, we gave them too much space and they scored two goals.
“The second-half was better, much more like performances I’ve been seeing and we can count ourselves a little unlucky.
“We were taking the game to Chelsea late on and asking questions of them to the point that they had to waste a bit of time at the end.”