It was Italy's second appearance in diving, with Carlo Bonfanti being the nation's only diver both in 1912 and 1908.
It was the third time the nation appeared in swimming, and both swimmers had previously competed in 1908.
Massa's second-place finish in his initial heat of the 100 metre freestyle was the only race in which either was not eliminated.
Nedo Nadi, the gold medalist in the foil, was also the only non-Hungarian to reach the final in the sabre, placing fifth.
None of the six advanced past the fourth round, as the team compiled a combined record of 8-12.