Though he was not a native of Rome, during the 15 seasons he played in the capital city, he was nicknamed "Core de Roma" (Romanesco for Heart of Rome). In total he made 450 appearances with the giallorossi, a record which lasted for 38 years, until 31 January 2007, when Francesco Totti played his 451st match for the club.
Losi started playing football for his hometown club, Soncino. In 1951, he transferred to U.S. Cremonese, and in 1955 to AS Roma where he made his first appearance on 20 March against Inter Milan.
He was a fullback with a playing style based on strength but also on fair play, in fact in his whole career he received just one yellow card. Though his short height (only 1.69 m) he was a great header and thanks to this skill he played many years as a sweeper.
He gained the nickname "Core de Roma" on 8 January 1961, during a match against Sampdoria in which the result was 2-2, Losi was injured but there were no more available substitutions, so he kept playing but succeeded in scoring the winning goal from a corner kick. For this reason Roma's supporters understood that even if he was not Roman, he was a great example of how people from Rome love their team.
He made his first appearance with the Italian national team on 13 March 1960 in a friendly match lost 3-1 against Spain. He was part of the squad that participated in the 1962 FIFA World Cup in Chile, playing two of the three matches of Italy. He has 11 international caps for azzurri.
He still lives in Rome, where he is the director of a football team, the "Valle Aurelia '87".
He is one of eleven members of Hall of Fame of A.S. Roma.