Newcastle lost 2-1 at Manchester City on Saturday.
Benitez was asked if Newcastle would stay up and replied: "For sure. It will be tough, it will be difficult but we knew the fixture list was difficult so it's a question of being sure we could be competitive. You can see in the games against Chelsea, Spurs and today we were competitive. I won't say what we did deserve or didn't deserve but we were close to getting something.
"That has to be a positive in terms of mentality, team spirit and work rate from my players. I'm really proud of my players."