The winger ended his five-year spell at the Allianz Arena this summer, turning down a contract extension after changing agents and opting for a fresh challenge.
Sane, who featured in over 220 games for Bayern Munich with 61 goals and 55 assists, turned down interest from other European clubs to join the Turkish champions.
"Diaz is a fighter and gives his all every minute. He's very good," Der Vaart told Ran "But I just think Sane's development is a shame. He threw his career away himself.
The Dutchman says the Bavarian will be fine without the German, as he backed Vincent Kompany to lead them to Champions League success: "Why not? I always find comparisons with other teams difficult. All top teams are at a good level.
“But to win the Champions League, you also have to be mentally top. After the previous season and their Champions League triumph, everyone thought Paris were unbeatable.
“And then they almost lost the Super Cup to Europa League winners Tottenham. They even suffered a defeat in the Club World Cup final against Chelsea."