The Magpies drew 0-0 with the Russian side in Moscow seven days ago and the manager hopes their chances of progression to the quarter-finals can capture the imagination of the club's supporters.
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"In the past, in the FA Cup and League Cup this season, we fielded sides that were not good enough. This side is good enough but we are up against some very good opposition."
Chelsea and Tottenham also remain in the competition and Pardew believes that, having often previously neglected the Europa League in favour of domestic priorities, English teams have a significant chance of success this season.
"I think the three teams in the Premier League can focus on the competition and that has not always been the case because of league titles or whatever," the Newcastle manager added.
"The experience that we are all gaining in this competition is helping the Premier League teams now. We have a responsibility for the Premier League and English fans, not just ours, to try to win this competition.
"Whether we have French, Italian, or whatever players playing for us it doesn't matter. We represent the Premier League and they are proud to represent the Premier League. We will try to fly the flag if we can."
The 51-year-old boss revealed that he had sought the advice of Brendan Rodgers, whose Liverpool team faced Anzhi earlier in the competition, ahead of the Thursday evening encounter.
"I spoke to Brendan about their two fixtures," Pardew confirmed. "We have done an analytical study of their games. We know all we need to know about them. That doesn't mean we can stop them.
"They have some outstanding players and have one of the best managers of the last two decades in charge but I still feel confident we can win. We go in to this with good confidence.
"Brendan was complimentary of their ability and their players in particular. He had a couple of warnings and thoughts he felt we could benefit from - no more than that."