Florenzi came on as a substitute in the 2-1 friendly defeat to France on Wednesday.
"Making your debut for the Nazionale is a unique emotion," he told Roma Channel.
"I am happy, as it was a dream come true. Singing the anthem before kick-off is also very exciting, stood there arm in arm with your teammates.
"It has all happened so quickly, but by staying humble you can achieve great objectives. Humility is essential."