"Gabriele was not violent, he was gentle and serene. So I ask all you young people not to commit any more violence," Tammi said.
Police have called the shooting of 26-year-old Sandri after a brawl between fans a tragic accident. But the incident has fuelled hatred between "tifosi" (fans) and police in the country which won the soccer World Cup last year.
Family and friends of Sandri, senior politicians and thousands of fans wore blue and white Lazio scarves, and also the colours of city arch-rivals Roma and other clubs, as his coffin arrived at the church in the north-west quarter of Balduina to traditional applause.
Francesco Totti, the captain of Roma and one of Italian football's biggest names, also paid his respects.
Giuliano Amato, Italy's interior minister, promised a thorough investigation into why a policeman fired two shots across a busy motorway at a carload of Lazio fans leaving a rest stop after a brawl. One of the shots killed Gabriele.
Vincenzo Giacobbe, police chief of the central city of Arezzo, near the spot where Sandri was killed, said tougher charges might be laid, with numerous witnesses saying the policeman had "probably" aimed at the tyres of the car that Sandri was in.
The policeman said that he accidentally fired the fatal shot as he was running, seconds after firing a warning round in the air.
One former high school classmate of Sandri's said at the funeral: "The policeman's gunshot was a man's mistake. Football has nothing to do with it."
Amato has also accused fans of using the incident as an excuse to go on the rampage around the country, setting fire to cars and attacking police stations, for which two Roman youths may face terrorism charges.
At least 40 police required hospital treatment after the running battles in several cities on Sunday which newspapers dubbed the return of the "nightmare" of hooliganism.
Italian police have made 25 arrests in the wake of the shooting death.
It was the second violent death linked to top league soccer this year after a policeman died in rioting outside a stadium in Sicily in February.
Some politicians want tougher action than the soccer federation's suspension of second and third division games this weekend. No top-flight matches were scheduled anyway, as Italy were playing Scotland in a European championship qualifier.
In February, all matches were suspended pending tougher security measures at stadiums after a policeman was killed in rioting at a match in Sicily.
The disparity in measures taken has led to accusations that officials take a policeman's death more seriously than a fan's.