The Paraguay striker came close to joining the Lazio only for the deal to fall through on the final day of the window.
Despite also being linked with Fulham, the 29-year-old Santa Cruz remained at City.
Santa Cruz, who is on international duty with Paraguay this week, said to Rome's Corriere dello Sport: "I had hoped to arrive in Rome, that was my dream.
"Unfortunately, the deal fell through. "There has been a lot of talk of my arrival to Italy and perhaps next time it will materialise."