Palace finished 12th last season but after a summer of limited spending Hodgson says he cannot be certain of any improvement.
Speaking at a Palace for Life event, Hodgson said: "Fans would like to hear 'yeah it's going to be a great season, we've finished roughly in the middle of the table the last couple of seasons, we're going to go on and do much better than that'.
"I would like to say that to you but if I'm realistic I'm not certain I can. I think staying in the Premier League is always going to be the be all and end all for us and always going to be a fight, a bit of suffering. There's not going to be rainbows and blue skies and rose coloured spectacles all the way through. There's gong to be plenty of fighting and heartache along the way."
He added: "I would like to think this club has a fanbase and a supporter base which isn't totally dependent on us being in the Premier League and getting into Champions League places because to be quite honest that's going to ask an awful lot of our owners to give the sort of money and financial backing that you need now."