The former Liverpool and Chelsea manager has been tasked with beating Juventus to the Scudetto and his side fired an early warning shot to the reigning champions.
Summer signing Jose Callejon scored on his debut and fans' favourite Marek Hamsik made sure of the points with goals either side of half-time.
While Benitez chose only to focus on his own team rather than Juve, he was pleased with the way they began their Scudetto challenge.
In quotes on the club's official website, Benitez said: "We do not think of others but only of ourselves.
"We are happy with the win and the three goals we have scored. We have created a lot and this satisfies me.
"We are just at the beginning but there are good signs for the future."
The Spaniard was not surprised by the display of his team, who finished second behind Juve last year.
"I was expecting this great performance," he said. "I was expecting a great game because the guys in the team have had a perfect training week.
"We have a department full of attacking quality, with so many offensive players who know how to play together and can go in goal "
"We are implementing a new and a different way of playing and the team is assimilating well.
"These indications for a coach are important because it means that everyone is convinced and determined what to do in the field."