Napoli, who beat Arsenal 2-0 on Wednesday night, looked like they would qualify for the knockout stages before a late winner for Borussia Dortmund in their game against Marseille sent Rafael Benitez's side out.
"It's difficult to explain how deeply disappointed we are. We're very sad because we wanted to stay in the competition," Maggio told reporters.
"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 turn their attention to the Serie A on Sunday when they host Inter Milan.