Palace's first league win over Chelsea in nearly 24 years provided a welcome boost in the Eagles' fight for top-flight survival, but, Jerome argued, will mean little if Tony Pulis' men do not now avoid defeat in south Wales.
"In respect of who it's against, it's a big win, but it means nothing if we go to Cardiff next week and get beat," Jerome said on cpfc.co.uk.
"We can't get carried away. We know we've got seven games to go and we've got to make sure we put in the same level of performance for the rest of the season and pick up enough points to stay in the Premier League."
Palace were praised for their performance by Chelsea boss Jose Mourinho and Jerome led the line well, asking questions of a Blues defence which conceded a John Terry own goal as the hosts won 1-0.
Jerome added: "It's a great result for us. The boys were fantastic. Everyone did their job and worked really, really hard.
"We created some really good chances in the second half and I think overall we deserved something from the game.
"We stuck to our gameplan and it worked. We frustrated them and they seemed to run out of ideas towards the end.
"We did well and luckily enough we managed to hold on and get the three points."
Jerome, who is on loan from Stoke, paid tribute to Pulis for his instructions, which the players then carried out brilliantly.
"The gaffer has set us up to play that way," Jerome added.
"He likes hard workers and he lets you get on with it in the final third. The likes of Yannick Bolasie, who was tremendous again, Jason Puncheon as well - as long as you put the hard work in going back and defending then he doesn't mind what you do going forward.
"It requires a lot of hard work, a lot of team spirit and a lot of effort from the boys.
"You've got to work doubly hard to ensure that if someone gets beat, you're there to cover them.
"We worked just as hard as we have over the last couple of games but we just didn't have the luck. That luck was there (against Chelsea)."
Mourinho conceded Chelsea's title hopes were over following the loss.
The Chelsea boss was critical of his players following a fifth away defeat of the season, believing key characteristics are missing in some of his stars.
Chelsea assistant boss Steve Holland agreed and insisted the shortcomings at venues where they should be winning must be addressed in order to sustain a challenge for the Premier League title.
"We've competed very well against all of the best teams consistently across the course of the year," Holland told Chelsea TV.
"It's not a coincidence. To be not just challenging and to be at the top and with a good chance of winning the league we have to do better across those games.
"We didn't do enough. When you look at the games where we've dropped points there is a thread of consistency across those games.
"It's something we have to address to make the next step."
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