The Rome club appeared to be close to completing a deal for the Turkish forward on deadline day, only for the transfer to fail to materialise after an apparent last-minute hitch in negotiations.
And Lotito has now revealed that the "extortionate" demands of the player's representative forced Lazio to pull out.
"A deal had been done with Galatasaray, you can phone their president and ask," he told Corriere dello Sport.
"Yilmaz would have cost us €13million 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."
Lotito also explained that Lazio held an interest in Fabio Quagliarella of Juventus and Liverpool striker Fabio Borini, but saw potential moves thwarted by circumstances beyond their control.
"A fee of €6m was agreed with Juventus and Quagliarella wanted us because he would have had more opportunities to play," continued Lotito.
"But Roma sporting director Walter Sabatini didn't give Marco Borriello to Genoa, so (Alberto) Gilardino stayed where he was (rather than joining Juve).
"His name was under consideration, but Liverpool didn't want to sell him outright and they preferred to keep him in the Premier League."
