The Magpies lost 2-1 to their local rivals but get an early opportunity to atone when Manchester City visit St James' Park for a fourth-round clash on Wednesday.
And Pardew said: "The derby was a really demanding game on the legs and on the emotions. We're disappointed for the fans and ourselves.
"But, if we could beat Manchester City, I think it would get people talking, because then we'd be down to the last eight and it all becomes a bit serious.
"I think any team in the Premier League can consider this a tournament they can win. 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 lost 4-0 to Manchester City in their first game of the Premier League season but Pardew thinks the visitors will be beatable this time.
"When they turn on their turbo chargers, with the players they've got, they're almost impossible to deal with," he said.
"But they're vulnerable as well and, particularly away from home, results haven't been as good as they would like.
"That is some comfort for us, that we could catch them on an off night.
"If your desire to win something is stronger than the opposition, then it does give you a slight benefit. We'll be leaning on that for sure.
"It's still tough to beat them. They have a squad of 24 international players, so we're coming up against 11 internationals, even if it is a slightly weakened City team."
Pardew plans to make a few changes himself, adding: "We'll be strong but we're in a run of three games in six days and we've got to make sure we're at full tilt for the Premier League games.
"I've got three or four players I feel need to come in and play, who have a chance of playing against Chelsea (on Saturday).
"It's an opportunity for players really close to the first team to make a stand for Chelsea. That question is in front of me: what team do I play versus Chelsea? I want a few people to give me a problem."
Watch Newcastle v Man City live on Sky Sports 1 HD from 7.30pm.