The Eagles defeated Watford 1-0 after extra-time in Monday's play-off final to seal their return to English football's top flight.
Delaney has a year remaining on his existing contract but remains relaxed about his future, and also about Palace's hopes of surviving in the Premier League.
The Irishman said: "People are going to say we are going to need to sign players, but I'll tell you what, team spirit will take you a hell of a long way.
"You look at the likes of the teams who have gone up, Swansea, Norwich, Southampton - they all went up and stayed up, and they didn't spend millions.
"They bought astutely and they kept the nucleus and the team spirit, which is what we have.
"What we are built on, to be honest with you, at Palace is that type of team spirit, that togetherness and the genuine friendship we have.
"We genuinely like each other. We wouldn't spend as much time as we do on and off the pitch - and believe me, we do spend a lot of time together off the pitch socialising and hanging out and going for dinner and whatever.
"If we can keep the basis of that and add to it, then the sky is the limit for us."
Palace's achievement is all the more special for Delaney, who started the season without a club after being released by Ipswich, and might have seen his career ended prematurely by a blood clot which formed in his leg during his time at Portman Road.
However, he has never allowed any of the setbacks he has suffered during his career to deflect him from his mission.
He said: "I have had a couple of injuries and a few other problems along the way, but it is just testament to perseverance, to be honest with you.
"If you just stick at it in the hope that some day, there will be a good day.
"There were some pretty low times there for me and I owe a lot to a lot of people who kept me going, family, a couple of good managers along the way, who keep you going and keep your head straight and keep you believing that there is quieter days out there.
"I am just a happy man and it is testament to perseverance, to sticking at it. If you stick at something long enough, you will get your rewards eventually."