Palace are in their seventh season in the top flight.
Hodgson said, “The obvious answer that fans would like to hear is: 'Yes it is going to be a great season, we have finished roughly in the middle of the table and we are going to go on to do much better than that'," said Hodgson. “I would like to say that to you. But if I'm realistic, I'm not sure I can.
“Man United, who have not had the greatest time the last two years, have probably spent close to half a billion pounds to get to that situation and of course our spending is nothing like that. For us, if it got above the hundreds of thousands from time to time, it would be nice.
“Staying up is going to be the be-all and end-all for us and there is going to be plenty of fighting and heartache. It is not going to be rainbows and blue skies all the way through.
“If I was going to leave any legacy at the club it would hopefully be: while he was here, the club played properly, the club did its very best to get results but most importantly of all, the club was every bit as strong – if not stronger – when he left as when he came. That would be my goal as manager of the club."