The 76-year-old will take charge of his boyhood club for a 200th Premier League contest when the Eagles host Chelsea on Monday night, Hodgson's side plunged back into a fitness crisis after the influential trio of Eberechi Eze, Michael Olise and Marc Guehi sustained injuries in their last two outings.
Their most recent result, a 4-1 loss at bitter rivals Brighton, ended in a heated exchange between two Palace players and fans in the away end, exacerbating an already strained situation that has in recent weeks seen Eagles supporters raise banners protesting the direction of their relegation-threatened club.
Hodgson said: "It's been the toughest period of my career for one reason, and that is that the fans have turned so much against us and they are the people that we cannot afford to have turned against us, because we need them.
"If we're going to win the games, and this team is going to do well, they're not going to be able to do it if the fans are going to be constantly up in arms about everything that's happening. Apart from that, it joins a lot of other periods of my life where I've been happier and more content, of course."
Hodgson has revealed he has not spoken with Palace chairman Steve Parish or sporting director Dougie Freedman about their "thoughts or plans" amid speculation they are actively seeking his replacement, and has taken a business-as-usual approach to his work.
His job will no doubt be made more difficult by the "devastating" news of Olise's most recent and "serious" hamstring injury, while Eze is ruled out with a hamstring issue of his own and his England team-mate Guehi will sit out what Hodgson hopes is a shorter spell after jarring his knee in the Brighton loss.
Despite appearing in just 11 of Palace's 23 Premier League contests, Olise has contributed six of their 26 goals, and against the Blades twice-assisted Eze, who has scored in five league meetings.
Altogether, the duo Sheffield United boss Chris Wilder recently conceded can "destroy your game plan" have been fit to start just four times together this campaign.
Throw in long-term injuries to defender Rob Holding and Cheick Doucoure, the latter feared absent for the rest of the season after undergoing surgery for an Achilles problem, a hamstring problem sustained by England youth international Jesurun Rak-Sakyi, alongside club captain Joel Ward's thigh issue, and Hodgson's once-dwindling injury crisis has emerged for an unwelcome encore.
The Eagles are aiming to secure Premier League football for a 12th straight season, but find themselves hovering dangerously close to the relegation zone with little hope of their injury situation significantly improving ahead of what could be critical encounters with fellow relegation-battlers Everton, Burnley and Luton over the next month.
Hodgson added: "One can only hope, encourage, ask the fans to stay with the team. We in particular need [them] now because we are in a very weakened situation, and we could do with their assistance and sympathy, because there will be players playing on Monday night that have not played that many games in the Palace first team.
"They're going to need a sympathetic eye rather than the ultra-critical."