The 27-year-old, on loan at Selhurst Park from Stoke, is one of only a handful of players at Ian Holloway's disposal who has plenty of Premier League experience to his name.
Following promotion through the play-offs last season, Holloway overhauled his squad and introduced no fewer than 15 new faces before the transfer window closed.
Palace, who have picked up just three points from their first seven league games and sit 19th in the table, face Fulham on Monday night with Jerome acutely aware that the players must believe they belong at the highest level.
"The most important thing is the transition from the Championship to the Premier League," he said.
"Quite a lot of the players haven't played at this level before and it is a learning curve so the sooner you adapt the better. Life in this league is tough and it holds no prisoners and can leave you blown away at times if you are not ready for it.
"We have to believe that we belong here and having the confidence and the arrogance to express ourselves on the football pitch in the right way, work hard for the team and do what has to be done."
A 3-1 win at home to Sunderland remains Palace's only positive result so far but they entertain a Fulham side who are also struggling in the early stages of the campaign.
Victory over Jerome's parent club before the international break means Fulham have seven points but remain 17th in the table.
Cottagers' boss Martin Jol has come under fire from a section of Fulham fans and Jerome feels Monday's game takes on a high level of significance for both sides.
"The importance of the game and to get something from it is huge," he added.
"Fulham haven't had the best of starts from what they would have expected so there is a bit of pressure on both sides.
"But, with us being the home side, we have got to take the game to them and we must come away with something from the game and the mindset around the squad at the moment is positive."