The 51-year-old saw Papiss Cisse snatch victory over Anzhi Makhachkala in the fourth minute of injury time to secure a place in the quarter-finals.
Pardew has predicted that an English club - Chelsea and Tottenham also progressed to the last eight on a dramatic night - could go all the way, and while he knows it would be a major achievement for the Magpies to end their 44-year wait for a major trophy, he believes they have a chance.
He said: "The question was asked to me and of course I think we can win it. But we can't get carried away.
"I do honestly believe that we have put one of the best teams out of this competition.
"If you ask me from the side of the pitch technically where do I pitch them, I would pitch them as a top-five team in the Premier League.
"They caused us a lot of problems. They have outstanding individual players in every area, really.
"We have beaten them, albeit with a slight bit of good fortune in this tie, so we can go on and win it.
"The one thing we do know is that the home tie here, whoever gets us is going to be in for another electric night.
"The fans played their part, they really did."