Edmund, 18, embarked on an impressive run of form to reach the semi-finals but could not keep that level going against the Italian.
The only two breaks in the contest were crucial ones, and both went the way of Quinzi in game seven of each set.
Unable to capitalise on the inconsistent first serve of his opponent, Edmund failed to find any breaks of his own and went down in straight sets.
Quinzi will meet Hyeon Chung of South Korea in the boy’s final, who beat Maximilian Marterer 6-7 6-1 6-3.
Edmund remains in the boy’s doubles draw.