Benitez's side beat Watford 1-0 at St James's Park last weekend thanks to a goal from Ayoze Perez.
The result saw the club climb out of the Premier League's relegation zone ahead of Saturday's home game against Bournemouth.
Benitez – who felt his team had deserved more from their opening 10 games – told of his relief at getting up and running.
“It was very important," said Benitez, speaking at the Newcastle United Foundation's 10 Year Anniversary Dinner at St James's Park.
"I was talking with some fans before, and I think everyone knows that in so many games, we were really close to getting that win.
"But we just couldn’t do it. So to get three points, even though the game was maybe not the best, was a relief.
"It means we are feeling much better and are ready for the next challenge."
Newcastle are 17th in the league ahead of the Bournemouth game.