The 24-year-old, who was making his first start since suffering an ankle injury against Chelsea on November 29, led the North London club to a 1-1 draw in the first leg of the last-32 tie at the Stadio Artemio Franchi.
"Obviously it's a proud moment for me and my family," Mason told Spurs TV.
"My family travelled out today so to have captained the side, I'm very proud and honoured to have had that experience.
"It's a massive responsibility, to be fair we've a lot of leaders on the pitch and I'd like to think I'm one of those.
"It was a great, great experience, obviously it was an important game, it was a tough game as well but I think it was a fair result in the end."
Very proud moment and an honour to captain the side tonight! An important away goal going into the game at the Lane next week! #COYS
— Ryan Mason (@RyanMason) February 18, 2016