Last Saturday’s 3-2 defeat at fellow strugglers Norwich left the Tyneside club six points adrift of safety ahead of this weekend’s trip to Southampton, with the current bottom three all expected to be residing in those places come the end of the campaign.
However, Benitez, whose three games at the helm have so far produced just a single point, is refusing to accept that the odds against a great escape are now overwhelming.
He said: “Everybody will say, ‘Oh, Newcastle will be relegated’, but that is normal when you see the table. At the same time, I can see the players changing in training.
“My concern would be if I saw the players giving up, and I don’t. I can see a lot of players working so hard in training, so I still believe we can change the situation.”
To do that, Newcastle may have to embark upon a similar kind of run to the one which saw current leaders Leicester win seven of their remaining nine games this time last season to drag themselves out of trouble.
Given that the Magpies have tasted victory just once in nine attempts and collected only one of the last 18 points on offer, that looks a tall order, although it is a hope to which Benitez is clinging.
He said: “I am convinced that we can do it.”
If Benitez’s side is to pull off the seemingly impossible, it will need more of the same from summer signing Aleksandar Mitrovic, who has scored three of his eight goals this season in the last two games.
Benitez said: “Sometimes for strikers to score goals, it’s the difference. With Papiss (Cisse) coming back from injury, he has more competition. Scoring goals will give him confidence and the competition of Papiss will hopefully also be good for him.”
Benitez, who will have left-back Paul Dummett back in contention after injury, but not skipper Fabricio Coloccini, will go into the game having brushed aside speculation he could be a candidate to replace outgoing Spain manager Vicente del Bosque.
He said: “I am the Newcastle manager and I want to be the Newcastle manager next year. I am really pleased here.
“Del Bosque is my friend – I was his assistant when he was with the first team at Real Madrid, he knows how I work. But still, I think I will be here for a while. I have confidence we will stay in the Premier League, so I don’t think about the other options.”