The midfielder ended months of speculation when he sealed his switch from PSV Eindhoven despite a number of European teams, including Manchester United, reported to have been monitoring his progress.
Milan were reported to be keen on bringing the 23-year old to the San Siro this summer, but Galliani says that the club were not prepared to meet PSV's asking price.
"He's a really great player. We followed him for a year too, but he cost too much and we left," he told Sky Sports Italia.
"At this moment, 20million euros is too much for Milan."
Galliani was also quick to dismiss suggestions that PSG striker Zlatan Ibrahimovic could be set for a Serie A return, believing that his wage demands would be too extortionate.
He added: "Ibra's return to Italy? I think it's absolutely impossible because he has a salary not compatible with the Italian league."
Robinho committed his future to Milan last week by signing a two-year contract extension, and Galliani revealed that the striker is now on lesser terms having failed to impress last season.
"He cut his salary and extended his deal," continued Galliani. "I told him that he didn't do too much last season and so he's like a new signing and he must show his value."