Sam Allardyce's men currently sit three points and two positions above the drop zone, with eight matches to go.
The outfit impressively shocked leaders Chelsea with a 2-1 win on Saturday, but found Southampton too strong in midweek, succumbing to a 3-1 reversal.
"The Premier League is one where anyone can beat anybody else and we know we are not safe until it’s done," Schlupp said, as reported by the club's official website.
"We are not a group of players to get carried away, we know we have a task ahead and go into every game looking to get ever nearer that final target to stay up.
"Confidence is a massive factor and the gaffer has put that back into us and of course going out getting results helps with that as well.
"The manager will have wanted things to change a bit quicker but we were not able to do that and now it is starting to work out well."
Since joining Palace on a four-and-a-half-year deal in January, Schlupp has made eight league appearances involving four starts.
He was on the books of Leicester City last season when the Foxes won the league for the first time ever.