Clyne says Palace are determined to do the fans proud by getting a positive result at Brighton on Monday night.
“Being at Palace before, I knew that this rivalry existed," he told Premier League Productions. “It means a lot to the fans and to the players.
“We're going to look to go into this game knowing that we've got to do it for the fans as well. We've had two disappointing results of late, but we've had a full week of training to correct things, to work on things.
“With the game coming up on Monday, it's a great opportunity for us to come back and try to get a win, and get a good performance as well."
Palace will be without Wilfried Zaha for the trip to the south coast, but Clyne says his teammates are ready to step up in his absence.
“He's a top quality player," he said, “everyone knows that. You can see this season that he's been fantastic for us with his goals and assists – his numbers are high.
“It's disappointing for him to be out injured because he's having such a great season, and we are definitely a better team with him in the side, but it's just about managing without your top player.
“The players who come in can do a job and we have to get results without him. At the end of the day it's a team game and you can't just rely on one player. It's all about adapting and playing, getting that cohesion and the run of form to get good performances."