The Magpies are currently in fifth place in the Premier League, just three points behind fourth-placed Chelsea in the race for a top four finish.
Pardew has now challenged his players to catch Chelsea and achieve with it a place in next season's Champions League.
"We've got to keep it going and chase down Chelsea," said Pardew.
"It's a great opportunity now and hopefully we can achieve something special.
"It's incredible. We're fifth and above Arsenal and Liverpool.
"We've got 39 points and we're safe so that's one job done. Now we've got 15 cup finals and it's all to play for."