Pardew admits he would love to deliver some silverware for their long-suffering fans.
He said: "We've had a tough season and it'd be nice for the fans to think we could win the trophy. I think we can, I really do.
"It would be a great achievement for this season because we've had injury crises for the most part and yet have managed to get through regardless of the injuries and that makes me proud.
"Thank goodness our Premier League form is improving and we sit here probably stronger than we have all season.
"But getting to the last eight wouldn't mean much unless we won it."