Dwight Gayle's first-half goal and a second-half brace from Ayoze Perez earned Benitez's men three points that secured them 10th place in the final Premier League standings and ended a run of four successive defeats.
The result gave Benitez revenge for the 3-1 defeat Newcastle suffered at Stamford Bridge in December 2017 and he called for owner Mike Ashley to invest in his squad this summer.
"It was a great way to end," he told reporters. "It was a perfect day for the fans and for everyone as it was a great atmosphere.
"I said before the game it is not about finishing 10th. We want to compete and with the right quality and at the right level.
"The players have done so well. We have to have confidence in this team."
The 58-year-old hopes to remain at the club next season, and said his squad would need reinforcements, especially with goalkeeper Martin Dubravka, striker Islam Slimani and winger Kenedy all set to return to their parent clubs when their loan deals expire.
"I still have one year left on my contract," he said. "The fans have ambitions, we have ambitions and if everyone has the same the potential is there.
"We have a couple of players on loan, some leaving so we have to sign players.
"You need competition to approach any game you want to win. You have to have a squad to compete."
Meanwhile, Ashley says he "hopes" Benitez will remain Newcastle manager after hitting out at those who have criticised his ownership of the club.
Ashley has echoed his previous support of the former Liverpool boss and his stance when it comes to investment.
"I would like to thank Rafa Benitez for his magnificent achievement this season," said Ashley. "I would also like to applaud the players, led fantastically by the captain Jamaal Lascelles.
"On many occasions throughout the season, they have been described as a Championship side, which I personally consider to be derogatory.
"Rafa, as always, has my full support, and contrary to some media reports that portray me as a pantomime villain, I will continue to ensure that every penny generated by the club is available to him.
"I hope very much that Rafa will remain at Newcastle United.
"Finally, I would like to thank the fans for their unrivalled support of Rafa and the team throughout the season."