Hatem Ben Arfa wasted a superb chance to grab a priceless away goal in a dour first-leg tie at a freezing Luzhniki Stadium, but Pardew was delighted to keep a clean sheet.
On next week's return clash at St James' Park, Pardew said: "I wouldn't say we are favourites because they have got good counter-attacking abilities in the team, but it's going to be a very different game at St James' Park.
"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."