Pato limped off during Wednesday night's 1-1 draw with Udinese at the San Siro, continuing a run of injuries that blighted his campaign last season.
He will now miss four weeks with a pulled hamstring and Galliani wants to find out why this keeps happening.
"This morning I called a meeting between the coach (Massimiliano Allegri), the fitness coaches and the medical staff to try to understand why a lad who in 2008 and 2009 never had any problems but now has broken down for the umpteeth time with a muscular injury," said Galliani.
Milan already had injury problems in attack with Zlatan Ibrahimovic, Robinho and Kevin-Prince Boateng all missing the game.
The club have had a poor start to the league season, picking up just two points from their first three games.
Apart from the Italian Supercup in August, Milan have yet to win a competitive game this season having also drawn 2-2 with Barcelona in the Champions League.
With one point less from their first three games, Inter Milan fired coach Gian Piero Gasperini and replaced him with Claudio Ranieri.
But Galliani insists the champions won't be making any knee-jerk reactions.
"When we get our injured players back we'll also rediscover winning ways," said Galliani
"It's not about luck or bad luck, we have 10-12 players injured, that's tough but it will pass.
"We won the title last season and the Supercup last month, it would be wrong not to stay calm."