The San Paolo outfit have enjoyed a fruitful season thus far, lying sixth in the Sere A standings and lagging behind joint-leaders AC Milan and Juventus by 10 points.
However, their exploits in Europe have been the talking point for Walter Mazzarri's charges, after they impressively navigated their way out of a Champions Group that featured Bayern Munich, Manchester City and Villarreal.
"We have done something extraordinary, we have accomplished something that was unthinkable," Gargano told his official website.
"Our goals for the New Year are to continue along this road, confirm our status and always aim to do better, especially in the Champions League.
"We are very united. As soon as we have a free moment, we spend it together, especially the South American players of the squad."
Napoli will now face off with London side Chelsea in a mouth-watering encounter in the Champions League last 16 knockout rounds.
Uruguayan international Gargano, who arrived in Naples in 2006, has featured 17 times in all competitions for Napoli this season.