The Eagles have made a decent start to the campaign, with two wins and a draw seeing them sit fourth in the fledgling table.
A 2-1 win away at Manchester United will live long in the memory while they entered the international break following a 1-0 home victory over Aston Villa.
Having ended up 12th in the standings last term, hopes were high that Palace might be able to push on and challenge for a top-10 berth but the loss of Aaron Wan-Bissaka to United plus the Wilfried Zaha saga meant it was an uncertain start to proceedings.
The Palace faithful will have been buoyed by the south Londoners' early points haul but Hodgson has been quick to temper expectations and made it clear that it is likely to be a tough road ahead.
"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', he told a Palace for Life event.
"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 was minimal investment in new players over the summer, with Jordan Ayew and James McCarthy arriving for transfer fees while Victor Camarasa joined the club on loan.
Experienced defender Gary Cahill arrived on a free transfer after leaving Chelsea and it remains to be seen if Hodgson uses some of the money from the Wan-Bissaka sale to strengthen his ranks in January.