Galliani said that the player could have left over the summer, but decided to stay and is now a big part of the club's future.
"I'd like to remind people that if we are in the Champions League, then part of the credit goes to El Shaarawy," Football Italia quotes Galliani as saying.
"He is only 20 years old and flew up the ranking, so growing up that quickly is difficult. Our judgment on him is absolutely positive, he has a five-year contract and we believe in him.
"He showed how much he cares about the club colours, because over the summer he could've moved to a team that was prepared to triple his wages."
El Shaarawy joined Milan from Genoa in 2011.