Although Angelillo was Internazionale's highest goalscorer while he was playing there, he did not win any titles with the "Nerazzurri". When the club appointed Helenio Herrera as the team's new manager, Angelillo's independent nature, rebellious character, and hedonistic lifestyle off the pitch led to several disagreements between the two; as a result, Angelillo was sold to Roma during the 1961–62 season, for 270 million lire, in spite of offers in Argentina from his former club, Boca Juniors.