The Magpies arrived in Ukraine after being held to a 0-0 draw on Tyneside last week, but despite losing midfielder Cheick Tiote to illness just before kick-off, they squeezed through to the last 16 thanks to Shola Ameobi's second-half penalty.
It was enough to lift the gloom on Pardew's worries over an ever-growing list of injury concerns and with the addition of five January signings, there is a belief the team can climb away from the drop zone and extend their European adventure.
Pardew said: "It's an important result for us. We lost Cheick just before the game, but Vurnon [Anita] did an excellent job coming in late. He only knew an hour before we kicked off that he was going to play.
"With [Hatem] Ben Arfa coming back and Cheick to add to that side, I really feel as though we can give this competition a good go."
Pardew revealed he had challenged Ameobi to raise his game before kick-off and got the perfect response as he claimed his 15th goal in European competition, a feat bettered only by Alan Shearer in a black and white shirt.
"I had a little quiet word with Shola before the game because, in the last few weeks, I thought his contribution could have been greater," Pardew added.
"But he's shown tonight what quality he has. Against this team, I always thought he might influence the game. He did that all night really and it bodes well moving forward."
A crucial visit of Southampton now awaits as Pardew prepares to face his old club.
He said: "We had some real heroes today and it's been a great week for us. We just need to repeat it on Sunday because that will be an important game.
"It could give us some breathing space in the Premier League, so we need to recover quickly. There will be changes for Sunday and hopefully we will get a result."