The hosts defeated Arsenal 2-0 but were eliminated on head-to-head goal difference, and the defender shared his deep disappointment at his side's narrow European exit.
The Partenopei scored twice in the second half against Arsenal in its final group game, but it finished third because of its inferior head-to-head goals record against the Gunners and first place Borussia Dortmund.
Maggio is gutted by Napoli's elimination but says that he and his fellow San Paolo stars are satisfied with their performances in Group F this campaign.
"It's difficult to explain how deeply disappointed we are. We're very sad because we wanted to stay in the competition," the 31-year-old told reporters after the match. "We showed that we are a real squad despite the criticism. Now we must keep working and think about the Europa League.
"Our group was incredible and we matched two fantastic teams. We are out but with our heads high and no regrets."
Napoli now turn its attention to Sunday's clash with Inter at the Stadio San Paolo.