The Magpies managed a 0-0 draw in the first leg of their last 16 tie with Anzhi, but the manager isn't convinced they will qualify, despite the second leg being at St James' Park
The former West Ham manager recognises the importance of the result, but is wary of being complacent against an Anzhi side that can punish anyone, citing the return leg at St James' Park as a tricky one.
The 51-year-old also called on his side to give themselves a boost at home to Stoke on Sunday afternoon, to set up a passionate atmosphere on Tyneside next Thursday.
"I wouldn't say we are favourites because they have got good counterattacking abilities in the team, but it's going to be a very different game at St James' Park," Pardew told reporters.
"But we really need to set it up on Sunday against Stoke. Sunday is something we need to put right.
"If we can get a win there, then I think the mood in our stadium is going to be something that's going to be very difficult for Anzhi to cope with.
"We didn't really have to fight the crowd today, and that probably helped us to settle. We got what we deserved tonight. We came and gave a really disciplined display.
"Rob Elliot had to make two good saves and really and truly, if someone had said that to me before the game I would have taken that. That's a really good display in the conditions and environment we were in."