The Eagles head to West Ham on Saturday without a win in the Premier League for 13 matches.
They still lie seven points clear of the relegation zone but Pardew insists they are not safe yet.
"We have a challenge in front of us," said the Eagles boss.
"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.
"Our desire and commitment can't be faulted but we need to turn that into one or two victories.
"It's a little bit easier when you have the points under your belt to look at other teams and say 'they'll be fine', but we're not.
"We're in a run of form in the league where we have no momentum and we are going to have to grind it out.
"We're not sleepwalking, we're not day-dreaming, we are fully committed to getting the points as soon as we can."
Source: PA