The result made it three wins on the bounce for the Magpies after defeat in their first two, and moves them up to fourth in the early standings.
"It is always good when you win and especially when the team is working so hard," Benitez told reporters afterwards. "Hopefully the fans are enjoying and the team can carry on winning. With this mentality it will be easy for us to win some games.
"At the end, we were suffering a little bit because we didn't take the chances we had. We had enough chances to manage the game a little bit better.
"What is important for us was to start winning and now it is to keep the momentum and make sure we don't play without confidence. We have to keep working hard and we know what we have in the team and the squad. Maybe we can lose games, but you still have to believe you can win."
Next up for Newcastle is a trip to fellow promoted side Brighton & Hove Albion a week tomorrow.