Norwich are just above the bottom three places, two points ahead of Sunderland and three clear of Newcastle.
With Aston Villa marooned at the bottom, two of the other three sides look like making the drop, just as a lucrative new television contract comes into being next season.
Norwich's Neil, in his first Premier League season after leading the team to promotion from the Championship last May,
claimed that the game was more important to the visitors.
"Looking at the table, Newcastle probably need to win the game more than us," he told reporters.
"But it would be an absolutely crucial win if we could go and get it," Neil added.
"I think they will approach the game with a bit of trepidation, and the first goal will be absolutely crucial.
"Another clean sheet would be a great, but it’s also about having that potent threat at the top of the pitch. Our home form in the main has been relatively good, so we’re going into the game confident."
Both managers agreed that the international break came at a bad time after their teams had just had shown an improvement.
Norwich followed a draw against Manchester City with a win at West Bromwich Albion, and Newcastle came from behind to draw their local derby with fellow strugglers Sunderland.
The internationals brought an injury blow for Benitez when Ireland goalkeeper Rob Elliot damaged knee ligaments against Slovakia and was ruled out for the rest of the season.
Karl Darlow, 25, is expected to make only his second league appearance for the club, having been blamed for the winning goal in his previous one against West Brom.
"We can't sign another goalkeeper, we have to support Darlow and I believe he has enough quality," Benitez said.
"The fans may think we have to win or it will be the end but I'm not convinced about that. We will go there to win but (after that) games are games."
(Reporting by Steve Tongue, editing by Ed Osmond)
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