Lotito admits he had an agreement with Gala for Yilmaz, before interference from a third party.
"A deal had been done with Galatasaray, you can phone their President and ask," Lotito told the Corriere dello Sport.
"Yilmaz would have cost us 13m in cash, plus a further 2m in bonuses. Everyone was in agreement, I was sure we could close and then I get an email from his agent.
"He outlined the details of the bonuses and salary agreed - 2.8m a season net. And then he asks me for a further 2m when the player signed.
"I was having none of it. It was extortion. It's the fault of a system that needs changing, I'm calling for new rules.
"I phoned UEFA President Michel Platini too. UEFA and FIFA need to act."
For the big stories and the banter follow us on Twitter: @tribalfootball