The Rossoneri vice-president says his coach's future is not dependant on the outcome of their next league fixture
While Vladomir Petkovic's Lazio have just Juventus and Napoli ahead of them at the top of Serie A, Allegri's outfit are trailing behind in 11th place.
Galliani attempted to relieve some of the pressure on the former Cagliari coach, insisting his job is safe and that he expects the team to improve following the conclusion of the international break.
"Whatever happens, Lazio-Milan will not be the last race for Massimiliano Allegri," the 68-year-old said at a sponsorship presentation.
"AC Milan is likely to be faster in the next games and the team as a whole will mature."
Claiming that Allegri's team had "not deserved to lose" the recent derby against Inter, Galliani suggested the Rossoneri are due "a little luck" when their league campaign resumes at the Stadio Olimpico.
The San Siro club will look for inspiration from the in-form Riccardo Montolivo, who scored Italy's first goal in the Azzurri's 3-1 victory over Denmark this week.
"He scored a nice goal in the derby [the strike was disallowed in the 1-0 defeat] and did well in the national team," added Galliani, who also confirmed that Alexandre Pato has recovered from injury and Sulley Muntari is back in light training.