Despite missing a chance to climb out of the bottom three following a 1-1 draw with Champions League semi-finalists Manchester City, Benitez claims Newcastle have put themselves in with a good chance of staving-off a second relegation in seven seasons, after taking four points from their last two matches.
They remain second-bottom, two points from safety going into the final month of the campaign as they bid to finish above Norwich and Sunderland to avoid the two remaining relegation places to accompany Aston Villa in the Championship next season.
Anita pegs Man City back to give Newcastle hope
Benitez insists his side will fight to the end after predicting the battle to avoid the drop will go right down to the wire. "Everyone is doing everything they can to try to stay up," he said. "Hopefully we have the momentum and we have to keep believing.
"We have more belief now and you could see that the players will fight to the end. I've told the players not to look at the league table too much, and just to concentrate on the next game. If they are concentrating too much on doing the numbers, they're wasting their time.
"That's two games in a row where we've had a great performance and had a great connection with the fans. To see the players perform like that with passion and commitment, hopefully we can keep that level in the final four games. We'll keep going and see where we are going into the last game, but with this kind of fight you have to be optimistic for the remaining matches."
Newcastle travel to one of the Spaniard's former clubs Liverpool at the weekend bidding to post a third game unbeaten.
Villa relegated as Sunderland, Newcastle boost survival hopes
Benitez has won one of his six games in charge since replacing former England manager Steve McClaren last month, and he added: "Liverpool are doing well in the Europa League and I wish them well in that, but hopefully we can go there and come away with three points."
Sergio Aguero's 100th Premier League goal put City ahead early on, but it was cancelled out as Vurnon Anita grabbed his first goal for more than two years before half-time.
Argentinian international Aguero became the second fastest player after the watching Alan Shearer to reach a century of Premier League goals -- in just 147 appearances -- and manager Manuel Pellegrini said: "I'm happy for him because it's not easy to score that amount of goals in such a short space of time. Hopefully he can keep scoring like that for the rest of the season.
"We did well because it was difficult with the great atmosphere provided by the Newcastle fans and their players were playing for their lives because of their place in the table."
City remain third, a point ahead of Arsenal and five better off than Manchester United. Pellegrini made only three changes, but hinted at more sweeping alterations to his side for Saturday's Premier League visit by Stoke City, which comes just three days before the last four Champions League clash with his former side Real Madrid.
Pellegrini added: "It's very important now that we make some rotations as we play this weekend and then against Real next Tuesday. We didn't play as well as we did in the victory at Chelsea, and that's maybe because we couldn't recover after playing so well at Stamford Bridge.
"Newcastle provided us with a tough test but we had chances to score a second goal to win the game."
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