The Magpies can reach the fifth round of the tournament on Wednesday night if they beat Manchester City at St James' Park.
"I think any team in the Premier League can consider this a tournament they can win," Sky Sports News quotes Pardew as saying.
"For the Champions League clubs, maybe it's a little down on their agenda, but it's high on our agenda. For us this year it is a priority. We want to win a trophy for our fans.
"If we could get past Manchester City, it would be a great way to put away the disappointment of Sunderland but that's easier said than done."
Newcastle suffered a 2-1 defeat at the hands of Manchester United in the third round of last season's competition.