Marseille finished last in the group with zero points.
"It just shows you in this group there were three very good teams," Arsenal coach Arsene Wenger said. "With Marseille taking no points at all, one team had to suffer."
Napoli will drop into the Europa League, while Arsenal joins fellow English clubs Manchester United, Manchester City and Chelsea in the last 16.
"It's incredible to exit after taking 12 of 18 points and getting them against the best English squad and the European runner-up," Higuain said. "I don't think that has ever happened."
Despite its group-stage success, Arsenal has never won the Champions League, losing the 2006 final to Barcelona being its best result.
Arsenal needed only a draw to be sure of advancing as group winners, while Napoli needed to win by a three-goal margin.
Wenger acknowledged some regret at not winning the group.
"Of course there is frustration. But it could have been worse tonight as well," he said then mentioned the streak of reaching the knockout round. "Maybe No. 14 will be good luck."
Napoli fans whistled when Arsenal had the ball, while the group of about 1,000 Arsenal supporters inside the visitors section at the San Paolo stadium was mostly quiet.
Wenger rested standout midfielder Aaron Ramsey at the start, using Tomas Rosicky instead on the right wing, while Napoli goalkeeper Pepe Reina missed the match with a right thigh injury, opening the way for 23-year-old Rafael Cabral to make his European debut.
Napoli took the initiative from the start with Goran Pandev and Higuain threatening in attack but the Italian side had trouble getting a good look at the net.
Arsenal was content to play more patiently and seized upon its first opportunity when Mesut Ozil set up Olivier Giroud for a blazing shot on goal, which Cabral did well to knock away.
Napoli continued to pour forward but Arsenal defended with 10 men and the closest the hosts' came to scoring in the first half was when a header from Higuain went wide in the 44th after a failed clearance by Arsenal goalkeeper Wojciech Szczesny.
There was a lull in action at the start of the second half, until Napoli left back Pablo Armero broke free and carried the ball into the area, only to shoot directly at Szczesny.
Callejon had another good look for Napoli in the 62nd but shot wide.
Ramsey came on for Santi Cazorla in the 67th but then Napoli took control, first with Higuain then with Callejon, who scored with a lob shot.
Despite the loss, Napoli fans gave their club a standing ovation as they walked off.
"In the first half we controlled well. In the second half Napoli was the better team," Wenger said. "They deserved it and overall when we were down to 10 men and 1-0 down of course doubt crept in and it was a difficult moment for us. But we managed to keep it to one goal until near the end."
Wenger acknowledged his side had difficulty weighing up whether to attack or defend.
"It's always difficult to cope with that problem during a game," the French manager said. "Napoli was sharper physically than us."
With Juventus also having been eliminated Wednesday, AC Milan was the only Italian club to advance.
Two Arsenal fans were slightly injured in minor clashes before the match, the ANSA news agency reported.
