Palace have failed to pick up three points in a top-flight match since December and have accumulated a worrying 13-game winless run, which includes nine losses.
"We have a challenge in front of us. The teams below us are now going to hunt points and hunt it down and unfortunately, we are in a position to catch, so we have to really up our game," Pardew told British media.
"We're not sleepwalking, we're not day-dreaming, we are fully committed to getting the points as soon as we can."
With eight game left to play, Pardew's side are 16th in the table, seven points above the relegation zone, and travel to face Champions League-berth chasing West Ham United at Upton Park on Saturday.