Three first-half goals at Selhurst Park gave Rangers a mountain to climb as Palace enhanced their own prospects of remaining in the Barclays Premier League with a 3-1 victory.
Matt Phillips pulled one back with a sensational 40-yard strike seven minutes from time but it will be of little consolation to Ramsey and his team, who remain entrenched in the bottom three.
Ramsey told BT Sport: “There wasn’t one player I could look at and say ‘they threw the towel in’.
“The only thing we can do is go back to the drawing board. The fact is we let ourselves down in key moments of the game and we need to take that out of our game.
“I wouldn’t say I am confident (of surviving) because I don’t think anyone below that line is confident, but we still have the willingness and we still have the players that can complete the task.”
Yannick Bolasie played a vital part in the Eagles’ first two goals, sending in a cross for Wilfried Zaha to open the scoring and also teeing up James McArthur to tap in the second before Joel Ward killed the game off before the break after good work in the build-up from Zaha.
Palace boss Alan Pardew hailed the impact of wide men Bolasie and Zaha, and told BT Sport: “I’m sure (former Palace manager and Manchester United winger) Stevie Coppell would have been proud today because down here we’re famous for our wingers.
“It was like a throwback today to an old Palace team and it was a great victory for us. When you have got players with the quality they have got – that I can’t coach. But what I can do is get them in the right place at the right time, where they should be and what they should do for the team and that’s all I’m trying to educate them on, and to score more goals.”
Asked about Palace’s position after this game, he said: “We are nearly safe. We need to just keep our heads, get ourselves another victory quickly and then we’re nearly done.”