Eagles fans also unfurled banners criticising Steve Parish and the board during their side's 4-1 defeat at rivals Brighton on Saturday - just as they had after losing 5-0 at Arsenal last month.

Palace were the top-spending Premier League side in January but have won just twice in their last 14 games in all competitions and sit only five points above the relegation zone.

• Brighton 4-1 Crystal Palace - Report and highlights
• Live Premier League table | Fixtures | Results
• Watch free Premier League highlights
• Stream Sky Sports with NOW | Get Sky Sports

Asked what it was like to hear Brighton supporters' taunts as Palace fans chanted for him to leave the club, Hodgson sarcastically responded: "Wonderful, wasn't it? What sort of answer do you want to that question?"

But the Palace boss - whose contract expires at the end of the season - says the criticism has not dampened his desire to fix the problems at the club, adding: "My years of managing have given me the resilience to cope with that.

"Taunts from supporters are part and parcel of our lives and, at the moment, our own fans are not happy with the way things are going so they're making their feelings known.

"But I signed up to be the manager of this club and I've got the strength, resilience and determination to see things through.

"I'm certainly not going to be cowed by that sort of thing and I'm certainly not going to give you the satisfaction of saying I'm hurt by that kind of thing because it's pretty obvious.

"Everyone wants to be liked, praised and told they're the best. When that doesn't happen, yes, it's a little bit hurtful."

Pressed on whether, at age 76, he still has the "appetite" for a Premier League relegation battle, Hodgson said: "Yes. I have no problem with that at all.

"I am very much behind the team. I know they are doing their level best and we're doing our level best to help them."

Hodgson defends players after clashes with fans

Hodgson defended the Palace players for going over to the away fans at full-time - something that prompted an angry response from many of the supporters that had remained until the final whistle.

Joachim Andersen appeared to get into a heated discussion with one section of the support and Hodgson admitted: "The fans are going to be very unhappy after seeing their team losing 4-1, so if you go over there you run the risk.

"You have to show the discipline not to bite back. I think the players did the right thing.

"We are happy the fans have come to support today. No one is less happy than ourselves with the result but at least they went over to thank the fans."

Hodgson also defended Parish, who helped to save Palace from administration 14 years ago, telling Sky Sports: "I think Steve Parish has done a fantastic job for the club.

"People's memories should be jogged. The club was in an awful state when he came with his partners at the time. They've turned the club around and got us into the Premiership and at the moment we're still there and fighting to stay there.

"It's not for me really to talk about the club structure and the ownership of the club - that's something you'd have to take up with Steve himself.

"But if you're asking me personally, as someone working for Steve Parish and the club, I think it's very harsh people are putting up banners in that way and trying to blame him for the fact we've lost a game against Brighton."

'I was told Olise was fit to come on'

Palace were already without Cheikh Doucoure and Eberechi Eze for the trip to Brighton, while Olise was not fit enough to start and Marc Guehi limped off during the first half.

Olise's status was doubtful due to a knock he sustained in the win over Sheffield United in midweek, while Hodgson has previously discussed the difficulties of balancing the demands of the team with his medical staff, saying he can't run the side "scientifically".

Olise was introduced at half-time but lasted less than 10 minutes before suffering a recurrence of his hamstring injury, but Hodgson defended his use of the winger.

"I was told that he couldn’t start the game and I was quite comfortable with that," Hodgson said. "They told me - and he told me - that he was fine to be on the bench and to play in the second half.

"Unfortunately I wasn’t to know that was going to lead to a recurrence of his injury. That’s exactly what we did.

"You can say ‘you were losing 3-0, why put one of your better players on?’ But it’s because we bought him all the way here to be on the field in the second half."

Analysis: Where do Palace go from here?

Sky Sports' Joe Shread at the Amex Stadium:

Crystal Palace are at a crossroads. For so long, mid-table stability, combined with developing a smattering of exciting young players, has been enough for the south Londoners.

Much of that stability has been provided by Steve Parish, whose backing helped to bring the club up from the Championship, and Roy Hodgson, who has done so much across two spells to keep the Eagles in the Premier League.

But now many of the supporters want more. Shorn of Eberechi Eze and Michael Olise for much of the season, Palace have slipped to just five points above the relegation zone, while winning just two of their last 14 games.

Hodgson's side have conceded nine goals in their last two away games, both of which saw fans turn on Parish and the board.

January's investment in Adam Wharton and Daniel Munoz doesn't appear to have placated the fanbase. With Hodgson aged 76 and only having a contract until the end of the season, a change in the dugout is surely coming sooner rather than later.

But what then? Palace only have the 12th-highest net spend over the past five seasons and have been missing arguably their three best players - Eze, Olise and Cheikh Doucoure - for huge chunks of the campaign.

Is it fair to ask them to be achieving any more than they already are? Palace supporters may want to be careful what they wish for.

Get Sky Sports on WhatsApp!

You can now start receiving messages and alerts for the latest breaking sports news, analysis, in-depth features and videos from our dedicated WhatsApp channel!

Find out more here...