The 20-year-old remains optimistic about his side's campaign, despite a poor start to the season that sees them sit bottom of the table after their opening 12 games
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The London outfit have also yet to appoint a permanent manager after Ian Holloway's departure late last month, with former Bristol City boss Keith Millen still in temporary charge.
But Williams - who has seen his campaign disrupted by an ankle injury - is confident Palace can overcome their difficulties and stay up.
"I still have faith we can turn it around as there is still over 25 games left to play and a lot of points to play for," he told The Croydon Advertiser.
"My personal targets are to get fit and stay clear from injury and then to try and keep Palace in the Premier League.
"We haven't been too far off getting a result and the performances have been very good in some games.
"Yes, we are bottom of the league at the moment and I imagine a lot of people have written us off already but that happened in the play-offs last year.
"No one thought we would get promoted but look what we achieved."
Palace travel to Hull City for their next Premier League clash on Saturday.