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 predicted yesterday 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 yesterday [Wednesday] 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 tonight, they really did."
Anzhi, who were reduced to 10 men 10 minutes into the second half when midfielder Mehdi Carcela-Gonzalez was booked for the second time in seven minutes, were more than a match for the Magpies on the night and came desperately close to scoring themselves with only two minutes of normal time remaining when Mbark Boussoufa's free-kick rattled the crossbar.
However, it was Pardew's men who finally broke the deadlock after 180 minutes and more of football in Moscow and on Tyneside when Cisse, whose 92nd-minute strike against Stoke on Sunday clinched three precious Barclays Premier League points, repeated the feat with a firm header, the last touch of the game.
The Newcastle manager said: "I have never experienced a game finish as late as that ever. [Assistant manager] John [Carver] came over and told me the game was over.
"I thought it was over before he [Cisse] scored, actually, for a horrible moment, so it was great that it was the last strike of the game."
It was Cisse's 10th and arguably most important goal of the season, and came from one of the few presentable chances his team-mates created on an at times frustrating evening.
Pardew said: "Papiss, as he did on Sunday, it's a chance that he perhaps could have made too much movement with his head and got it wrong.
"But he just waited, he was calm and that's what goal finishers do. They are calm at that crucial moment."
Pardew and his players will now await tomorrow's draw in Nyon with eager anticipation after extending their adventure by reaching the quarter-finals of the competition for the first time since 2005.
By contrast, Anzhi boss Guus Hiddink headed back to Russia bemoaning his side's fortune, but consoled by the performance at St James' Park.
He said: "I was just asked if the result was justified or fair and I told them, 'It's not a jury sport'. If I would have had a jury tonight [Thursday], I think we would have won unanimously.
"But it's not about the good play we did, it's also to be effective and they proved in the last and, I think, one and only open chance, that they got their result."