Palace secured promotion to the top flight with victory over Watford in the Championship play-off final.
McCarthy and his team-mates take on Tottenham in their opener on Sunday and he says the whole squad are excited about the big kick-off.
"Obviously we are excited at what is ahead of us and we can't wait to get started," McCarthy told Sky Sports News.
"We are going to enjoy every week and we are going approach it with no fear.
"We have worked long and hard to get here and we have earned the right to be rubbing shoulders with these top players and top clubs.
"We are going to enjoy ourselves first and foremost, play with a smile and with bags of enthusiasm, give 100 per cent and hopefully by the end of it we will have retained our Premier League status.
"We have our own ambitions and we are going to work tirelessly until May to try and retain our status as a Premier League club."