Ayoze Perez's first-half header, his seventh league goal of the season, was enough to settle a tight match at the King Power Stadium on Friday.
Newcastle moved up to 13th as a result and they seem certain to have preserved their Premier League status for another year.
But Benitez's future at the club remains unclear, with the Spaniard having regularly indicated he is unhappy with the lack of investment in his squad.
Benitez's contract expires at the end of the season and he has compared talks with controversial club owner Mike Ashley to Brexit negotiations.
"I have been trying to win titles everywhere, in different countries," Benitez said to Sky Sports.
"We have to have a team who can compete. This city, the club has potential. It's massive. I'm not looking to spend £200million, but doing the right things.
"You can do everything right with your tactics, but the other team has one player that can make the difference. You'd have to pay £30m to buy a Leicester player."
Leicester completed 649 passes but Newcastle goalkeeper Martin Dubravka was not tested too severely and Foxes boss Brendan Rodgers accepted his team need to be more ambitious on the ball and precise in possession.
"It's difficult to break down a team like that, it's an area we will get better at," Rodgers said after his side's four-game winning run ended. "There wasn't a lot in the game, our final pass just wasn't there but we gave everything. We couldn't break down their defence.
"We will learn from it: this is why I am here. Games like that you have to stay patient and have tactical discipline. The players have been first class since I came here but if you're not quite on it a result like this can happen.
"The speed of our passing in particular can be much better. We let them get into shape too early. It needs to come quicker. We changed it around a few times but it was one of those evenings. It will be good for our learning going forward."