The Italy international, who joined the Saints from Roma in the summer, got off the mark for them in the 2-0 win over Crystal Palace on Saturday.
"I was waiting for this goal since I started to play and I'm doubly happy because of the goal, and also because we got the victory," the 27-year-old told Southampton's official website.
"I was happy with this and as I have said before, I will be doing everything to score to help us in our next matches."
"Not only for the goal, but since I arrived here, the fans have been fantastic with me. They show me every time their love for me and I wanted to start paying back with goals if possible, but if not, then with attitude on the pitch."
Southampton currently sit in fourth place in the Premier League table.