Napoli were trailing 1-0 from the first leg heading into Thursday's encounter at Stadio San Paolo, but looked on course to overturn that deficit when Goran Pandev latched onto fellow forward Higuain's throughball and calmly finished past Porto goalkeeper Fabiano.
The hosts pressed for a goal that would have put them ahead on aggregate, with Lorenzo Insigne's close-range header that drew a point-blank save from Fabiano the pick of the chances.
Porto had failed to produce much in terms of clear-cut opportunities, but a quickfire double turned the match on its head, as Nabil Ghilas - who also scored the goal that sent his side into the last 16 on away goals against Eintracht Frankfurt - levelling on 69 minutes, before Ricardo Quaresma's fine solo effort put Porto ahead seven minutes later.
Napoli drew level on the evening thanks to Duvan Zapata's close-range strike in injury time, but the damage had already been done.
Higuain believes that Napoli were unlucky to exit the competition, but feels there is much to play for this campaign, with Rafael Benitez's men challenging for second place in Serie A, as well as facing Fiorentina in the Coppa Italia final in May.
"We put in a good performance and created so many chances, so we deserved to go through," Higuain told Mediaset.
"Their goalkeeper had a great game. Our season does not end here, as we have to look forward and the applause of the fans proves that. Our season does not end tonight."
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