The Magpies edged out Anzhi Makhachkala on Thursday to reach the last eight, with a dramatic late effort from Papiss Cisse seeing them to a 1-0 aggregate success.
Pardew feels anything is now possible, with Newcastle having found form towards the end of a largely disappointing campaign.
"Of course I think we can win it," he said.
"I do think we've put out one of the best sides in the competition. I would say they'd be a top-five team if they were in the Premier League and we've beaten them, albeit with a slight bit of fortune.
"We can go on and win it. The one thing we know is that whoever comes here is going to be in for another electric night."
Pardew saw Cisse net his 10th goal of the season in midweek, with the Senegal international having seen his fortunes turn alongside those of the club.
The Magpies boss added: "It's not that we've had to persevere with him, that's probably not the right word to use. But he's a natural goalscorer and he's got to be given chances. He's not been blessed with a lot of them.
"This week he's had two really good chances and he's scored them both.
"I know one thing - his mood, like with all strikers, changes with goals. But he does a good shift for us."