Navas completed the full 90 minutes on Friday, as Madrid crushed Manchester City 4-1 in the International Champions Cup in Melbourne.
The Costa Rica international made just six appearances in La Liga last term, with Iker Casillas regularly getting the nod in goal from former coach Carlo Ancelotti.
After Casillas' departure to Porto, Benitez has backed Navas to be first choice at the Santiago Bernabeu ahead of Kiko Casilla - a recent recruit from Espanyol - potentially signalling an end to the club's pursuit of De Gea.
Asked if Navas has the quality required to be a regular starter, Benitez said: "I think so, yes, we wanted to give him the chance to play and prove himself and he has done well."
When pressed if he needed another goalkeeper, Benitez gave a hint that De Gea would not be needed.
"I only need one goalkeeper on each match, and as long as I have one, I'm happy," the 55-year-old said.
Another Madrid player looking to convince Benitez he is worthy of more opportunities is Denis Cheryshev and the Russian winger did his chances no harm after scoring his first goal in the win over City.
The 24-year-old spent the past two seasons on loan at Sevilla and Villarreal respectively and was thrilled to have scored in front of Benitez.
"I'm okay, very happy and trying to make the best of the opportunities than I'm given, and I go home happy today after scoring a goal," Cheryshev said.
"I'm at the club's disposal, whatever they say I'll do and that will be okay."
Asked if Benitez had hinted if he would be needed in the senior squad, Cheryshev added: "No, I believe that Rafa is really focusing on all of us. I'm very thankful as I see he's very kind to me."