Athletic spurned a handful of clear chances before Marek Hamsik put the Serie A side in front at the San Mames in the second leg of their playoff clash on Wednesday.
However, Aduriz scored twice in 10 minutes to turn the tie on its head before Ibai Gomez sealed the win and a return to Europe's elite tournament after a 16-year absence.
And Aduriz feels their determination to attack throughout the 90 minutes was the decisive factor, telling Sport Mediaset: "I think the team worked very hard and we did not lose our heads after going a goal down at home. It is one of our characteristics, that we never give up and never stop attacking.
"I think Napoli are a great team and they made life difficult for us, but we trusted in our own strengths and came through in the end."
Head coach Ernesto Valverde, meanwhile, paid tribute to the raucous San Mames crowd for helping to roar the home side into the group stage.
"Of course we kept calm, as we had prepared for a difficult game against a great team like Napoli," he said.
"The difference was made by the crowd at the San Mames, as they helped push the players on and we kept faith in ourselves.
"It's true no Italian team has ever won at the San Mames. This is an historic day for us - 16 years on we are going into the Champions League."