Palace had lost nine out of their ten matches so far this season and had failed to keep a clean sheet, yet Everton failed to create anything more than half openings at a gloomy Selhurst Park.
Roberto Martinez had named an unchanged side from the one that drew with Spurs last week, meaning Leon Osman keep his place ahead of Ross Barkley.
The visitors, perhaps unsurprisingly, dominated the early possession but in what became a theme of the afternoon, failed to do anything with it.
The only chances of note during the first period was a mis-hit shot by Osman that was very nearly glanced in by Romelu Lukaku and a Kevin Mirallas long-range effort pushed wide by Julian Speroni.
Everton’s failure to stamp their authority on the game saw Palace grow in confidence and they really should have been ahead at half time.
First Kagisho Dikgacoi somehow contrived to head the ball away from goal when free at the far post before Tim Howard did well to palm away a curling effort from Jerome Thomas.
Marouane Chamakh then planted a header wide when well placed, meaning Everton went into the break counting their blessings.
The hopes was that the Toffees would respond to those Palace opportunities and take a grip of the game in the second half but it simply did not happen.
Indeed they were fortunate not to fall behind again when Thomas beat the offside trap and got one-on-one with Howard, but could only loft the ball up and into the side netting.
Palace, to their credit, worked extremely hard and were buoyed by the backing of the long-suffering home support, who were sensing a welcome point.
They understandably tired in the final 20 minutes and dropped deep, but Everton failed to take advantage, with the introductions of Barkley and Gerard Delofeu failing to change the tide of the game.
The only real opportunity came when Phil Jagielka hit the bar after Cameron Jerome had inadvertently flicked on a Leighton Baines corner.
It was agonising to watch as the players refused to up the tempo. All too often it took three of four players to find a player in space when he could have been found in one and there was a reluctance to have a shot or put the ball in the box.
Martinez’s style is easy on the eye and great when you are already in front, but sometimes it makes it easy for the opposition to play for the draw.
The cheers from the home crowd at the final whistle summed up their opinion of the game, while certain members Everton’s disgruntled support made their feelings known.
Distin, who, to his credit, always fronts up, came over to the fans and appeared to want to speak to one supporter in particular, seemingly indicating that his criticism was unfair.
I can see both sides of the argument n this one. The fans paid a lot of money to go all the way down to Selhurst Park and should expect better against what is an average Palace team. However, sometimes the criticism levelled at the players can go too far, particularly when it comes to individual or personal abuse.
I think Distin just had to accept that such criticism comes with the territory and remember that those some individuals who hurl abuse at him will be singing his praises if he scores against Liverpool next week; its not necessarily right but is the way it is. At least he showed he cared.
For the team it is another disappointing result going into the international break but one that could easily have been worse. It seems that Everton struggle when playing a side who are content to defend and play for a draw, meaning Liverpool could be the ideal opposition when the Premier League resumes in a fortnight.