Jonjo Shelvey scored twice and there were also goals for Ayoze Perez, Ciaran Clark, Aleksandar Mitrovic and Grant Hanley as the Magpies stormed to their fifth consecutive win.
It was a club-record home league defeat for beleaguered Rangers, who were completely outclassed.
But Benitez said: "We can still improve. The team was playing well, everybody was pushing and working hard, but you always make some mistakes.
"The main thing for us was to get the three points so we could leave our fans happy. We also managed to get the clean sheet.
"We now have to show we can concentrate in every game. It doesn't matter if we score six goals, we get three points in the end and now have to concentrate on the next game and not lose that concentration."
The victory came after striker Dwight Gayle, who has already scored four goals this season, was left on the bench, with Mitrovic returning to the side.
"I'm very happy with the strikers," Benitez said.
"Gayle is playing well, Daryl Murphy is doing well, so to play someone else is always difficult.
"I'm really pleased because we have a good squad and everybody has to be ready to be key players for us for the rest of the season.
"To have to decide between Gayle, Murphy and Mitrovic is a good problem, but it is a problem - it's not easy to keep everybody happy.
"Hopefully we will keep winning and they will understand that it is all for the good of the team."