The Magpies are second from bottom, four points adrift of safety, though they have two games in hand as they prepare to host Sunderland in Sunday's Tyne-Wear derby.
But Benitez, who replaced Steve McClaren last week and oversaw a 1-0 loss at leaders Leicester City, feels Newcastle are capable of much more.
"I decided to come because I knew how big this club was; the fans, the stadium, everything. You can see that it's a sleeping giant," Benitez said.
"Then you think maybe with your experience and talking with everyone at the club, I can see that if we stay up, we can achieve things because the potential is here."
Benitez, who signed a three-year contract, believes his side can survive relegation to the Championship.
He said: "At the moment, my job is to give players confidence, to win games, and to stay in the Premier League. I think that we can do it; still I think that we can do it.
"Obviously if we win this game, it will be easier for everyone because it will give them more confidence and help them to work hard and do really well, so then we will have more confidence and believe that we can do it.
"I think if we stay up - and I am sure we will stay up - then we can improve a lot."