Alexandre Lacazette had given Arsenal an early lead at St James' Park but goals from Ayoze Perez and Matt Ritchie gave Newcastle their fourth consecutive win.
Benitez had stressed that 40 points was the target after victory over Huddersfield two weeks ago, and as Newcastle reached that total he was happy to admit that his aim had been met.
"I think we are safe with 41 points," Benitez told his post-match press conference, quoted by the Newcastle Chronicle. "It’s a massive achievement for the players, the city and the fans. I want to congratulate everyone.
"We started learning without too much experience for some players in the Premier League, and little by little we were growing and especially in this second part of the league, the team has grown in confidence."
Defeat to Liverpool at the start of March had left Newcastle teetering just two points above the relegation zone and in danger of an immediate return to the Championship. But wins over Southampton, Huddersfield and Leicester had eased those worries before Sunday's win put any remaining doubts to bed.
“We were so good in a lot of things that in the end, I think we deserve to be where we are," added Benitez. “Some people were dreaming that maybe we could be here, but they were not awake.
“We were awake, we were believing from day one and we have achieved what we wanted.”
Benitez is a popular figure on Tyneside and his name was chanted throughout the match by Newcastle fans, who are desperate for him to remain at the club despite a fractious relationship with owner Mike Ashley.
The Magpies are now chasing a top-half finish, and they travel to Everton next Monday.