Steven Davis hit the victor in only the sixth minute at Selhurst Park and Fraser Forster made good saves to deny Christian Benteke and Jason Puncheon, as Palace became the first team in the history of England's top division to lose their opening five games of a season without scoring a goal.
The former England and Fulham manager oversaw his first training session at Palace's Beckenham training ground yesterday after signing a two-year contract to succeed Frank de Boer.
The former Liverpool manager said the division had "evolved" in the five years since he was last a Premier League boss but he remains convinced he will lead Palace to safety.
"As far as I am concerned, it is, Crystal Palace, Crystal Palace, Crystal Palace, it's everyone at the club, hierarchy, players, chairman and owners and most importantly perhaps of all, the fans". Wilshere was one of Hodgsons most utilised players during his time as England manager, selecting the midfielder 29 times from his 56 matches in charge.
I am sure we will see some changes in Palace in their upcoming games but, after about 10 matches under Hodgson, we will be able to see a big difference. I think we should have scored another goal but I am happy with the performance.
Speaking after the defeat, Hudgson said: "We didn't deserve a fairytale ending".
"I have very good memories of those times and the people I worked with and the players I worked with, but unfortunately, it's over". He has local ties, played for the club at youth level and was available now.
The home side applied the pressure in the second half but Mauricio Pellegrino's side were largely untroubled late on as they recorded their second win of the season and left Palace rooted to the bottom of the table.
Roy Hodgson admitted he faced a stiff challenge to turn around Crystal Palace´s fortunes.
Crystal Palace have confirmed that Orlando Trustfull, Sammy Lee and Ryland Morgans have stepped down from their respective positions at the club on 16 September.