Michy Batshuayi's goal was his first in the Premier League since he netted a double for Chelsea against Watford in October 2017
Leicester boss Claude Puel said "it is normal for the fans to be worried" after his side suffered a 4-1 defeat to Crystal Palace in the Premier League.
It was the first time in 19 years Leicester have lost four league games in a row at the King Power.
They have also gone six games without a win and have conceded the first goal in 19 matches, more than any other team.
"I understand the fans' feelings, they are disappointed," said Puel. "It is a difficult period for my team."
"I would like the fans to keep their support for the players, to support all these young players in the next game. At this moment we are unlucky. They have the feeling that they are not getting fair results.
"When we look at just the results it is not enough, it is not normal. But when we look at the performances it is crazy in this period. It is difficult to accept.
"I manage the pressure, the most important thing is my players," he added.
Wilfried Zaha scored twice as Crystal Palace eased their relegation worries on a day when Roy Hodgson became the oldest man to manage in the Premier League at 71 years and 198 days.
In a first half of few chances, the Eagles broke the deadlock when Michy Batshuayi fortuitously deflected James McArthur's effort past Kasper Schmeichel.
Jonny Evans fired home Harvey Barnes' low cross to equalise midway through the second half before Zaha ghosted in at the back post to retake the lead for the visitors.
Luka Milivojevic then scored from the spot after Evans clumsily brought down Jeffrey Schlupp and Zaha added a fourth in injury time to make the points safe for Hodgson's side.
Eagles take their chancesWin thanks to solid defensive display - Roy Hodgson
While Leicester took 14 shots in the first half alone, Palace only needed seven to score their four goals.
It is the ruthless streak the Eagles had been missing so far this campaign, and the sort of efficient finishing that perhaps could have seen them pull away from the drop zone weeks ago.
However, having now put together a four-game unbeaten run for the first time in the Premier League this season, any relegation worries have been well and truly eased.
Batshuayi opened the scoring with just their third shot on goal, as he instinctively powered home McArthur's volleyed effort.
Zaha added another after Evans had handed the hosts a lifeline as he calmly volleyed past Schmeichel before Milivojevic dispatched from the spot.
Zaha then netted their fourth - finishing off a lightning counter which epitomised Palace's performance - deep into injury time with the tiring Leicester defenders and a frustrated Schmeichel already well beaten.
It will be a game Hodgson and the Eagles faithful will cherish.
Lacklustre Leicester struggle againLeicester 1-4 Crystal Palace: Defeat difficult to accept - Claude Puel
Given Leicester have now conceded the opening goal a league-high 19 times, history suggests the Foxes are often slow starters.
But against the Eagles they began the game in encouraging fashion, dominating both possession and territory.
James Maddison, Youri Tielemans and Harvey Barnes all tried their luck from range as the Foxes racked up 27 shots on goal, but none of their efforts seriously tested Vincente Guaita.
Jamie Vardy went close when he headed Barnes' wicked cross over the bar while Mamadou Sakho did well to block a vicious strike from Maddison.
But for all Leicester's efforts it was Palace who struck first - with only their third shot of the game.
The hosts continued to press following the break and they did eventually get their reward as Evans blasted home the impressive Barnes' low cross after 63 minutes.
But they had no answer to Zaha's first and they crumbled when Milivojevic added a third.
Defeat means the Foxes have equalled a club Premier League record of four straight home defeats with pressure mounting on Claude Puel.
Man of the match - Luka Milivojevic (Crystal Palace)The Eagles skipper stood out in the middle of the park - he took 47 touches and made 30 passes, as well as a team-high three tackles'We put away our chances' - what they said
Crystal Palace boss Roy Hodgson on BT Sport: "It was a very important victory for us. We dug in extremely well and didn't concede many clear-cut chances.
"I was really pleased with the way we established control in the second half and we put away our chances. You do need to maximise the chances that come your way."
Eagles goalscorer Wilfried Zaha, speaking to BT Sport: "It is a massive result. Obviously we're trying to keep the run going and we came here and did what we had to do."
Leicester manager Claude Puel on BT Sport: "I think we made a good performance in the first half with good chances and good play, and then conceded the first goal with their first shot.
"It was difficult to find a solution because they played and blocked but we tried a lot of good moves.
"We came back with desire in the second half but after the second goal we did not manage the game right. It was difficult to have structure and stop the counter attack."
Batshuayi's big five - the stats
Crystal Palace have won four Premier League away games against Leicester; against no other side have they won more (also four v Everton).Crystal Palace striker Michy Batshuayi scored in the Premier League for the first time since October 2017 (for Chelsea v Watford), 490 days ago.Since the start of the 2014-15 season, no player has scored for more different clubs than Crystal Palace's Michy Batshuayi in the big five European leagues (5 - Marseille, Chelsea, Borussia Dortmund, Valencia and Crystal Palace).Leicester goalscorer Jonny Evans became the fourth Northern Irish player to make 250 appearances in the Premier League (also Aaron Hughes, Chris Brunt and Steven Davis).Crystal Palace midfielder James McArthur assisted two goals in a Premier League game for the first timer ever (232 appearances).Crystal Palace's Wilfried Zaha has scored in three consecutive league appearances for the first time ever.Since his debut in February 2017, Luka Milivojevic has scored 20 goals for Crystal Palace; more than any other player.What's next?
Leicester welcome Brighton to the King Power Stadium on Tuesday (26 February, 19:45 GMT). Meanwhile, Crystal Palace host Manchester United the following night (27 February, 20:00).
