Sneijder was frozen out by Inter coach Andrea Stramaccioni after refusing to take a pay-cut.
"Stramaccioni had to do what he had to do," he told Volkskrant. "He has a great opportunity at Inter.
"It was not his fault. I have always had a good relationship with the club and the President.
"I realised, at a certain point that I had to leave. But I took responsibility, as I always do.
"I am happy now. Galatasaray is a great club. I knew I had to come here - there's not point crying over the past."