The Italians gave away two goals in the opening 15 minutes to lose 2-0 at Emirates Stadium in their Champions League Group F game.
The result was Napoli's first defeat of the campaign, and Hamsik told Sky Italia: "We have to compliment Arsenal. They deserved the win.
"When you come up against a team like this one, there are differences.
"We knew of Arsenal's quality, how they enjoy to control possession and you can only beat them if you play in the same way."
Hamsik believes his team should have done better, especially early on.
"You cannot start a game in the manner that we did," the Slovakia international said.
"We gifted them with 15 minutes and two goals.
"After that, it becomes difficult to take a positive result against a team like Arsenal.
"They were just devastating early on and we were terrible."
Napoli were hindered by the absence of Argentina striker Gonzalo Higuain, who failed a last-minute fitness test.
"Higuain is an important player," Hamsik said.
"But there are others who filled in and we should have done better.
"We can certainly learn and improve from this."
Napoli, who are third in the group, three points adrift of leaders Arsenal, travel to France to face Marseille on October 22.