Hodgson's side travel to Craven Cottage this weekend in fine form, with the club unbeaten in five pre-season fixtures.
However, Hodgson told Palace TV he expected significantly tougher tests ahead for his side with the season about to begin.
Speaking after Palace's 4-1 victory over Toulouse, Hodgson said: "We have 38 tough games to come, the moment we start kidding ourselves its not going to be that way will be a major mistake.
"And in particular playing a team like Fulham, who have been out of the league for four years, but have now come back to the place where I believe they belong, so it will be a big occasion with a fantastic atmosphere and we will be put to a severe test that day.
"I am just hoping that the good stuff we have experienced in this pre-season will stay with us and we will find the extra edge to our game that we may need to compete with a Premier League opponent as opposed to those we have met so far."
Hodgson managed Fulham between 2007 and 2010, guiding the club to its most successful period in the Premier League era which culminated in the club reaching the Europa League final in 2010.
The 70-year-old joined Palace early on last season with the club bottom of the table following the sacking of Frank de Boer, going on to guide the Eagles to an impressive 11th-place finish.