Stretching back to the end of last season, they have now gone six consecutive league games without a goal for the first since January 1995 (a run of nine) and have had three different managers in that time - Sam Allardyce, De Boer and Hodgson.
Even if Palace improved on their previous showings, they remain bottom of the table and with league fixtures against Manchester City, Manchester United and Chelsea to follow in the coming weeks.
And he got to meet his inherited squad for the first time less than 24 hours later at the club's Beckenham HQ as they prepared for Saturday's visit of Southampton.
"On the psychological aspect, we have to make sure people don't dig themselves into a grave", Hodgson said.
"You have to fight for every single point".
"But it's a chapter that's finished, in the past as far as I'm concerned, and now it's a chapter in the book of life opening for me, and one I'm looking forward to, one I'm hoping brings joy to the fans of Crystal Palace".
― Reuters picLONDON, Sept 16 ― Roy Hodgson admitted he faced a stiff challenge to turn around Crystal Palace's fortunes after a 1-0 home defeat to Southampton saw them become the first Premier League side to lose their first five games and fail to score. "We could have scored another goal but playing here is really hard".
Mauricio Pellegrino, Manager of Southampton during the Premier League match between Southampton and Watford at St Mary's Stadium on September 9, 2017 in Southampton, England. They created a couple of chances at the beginning but after that I don't remember too many clear chances for them. After the goal, you could see the nerves and the anxiety.
The south London club lost their opening four Premier League games without scoring a goal, the worst start to an English top flight campaign for almost 100 years.
Steven Davis scored his first Premier League goal since May 15 2016 - also against Crystal Palace.