After failing to agree terms with the cash-strapped Ibrox club, the 31-year-old completed his move to Turkish title winners Bursaspor on Friday by signing a two-and-a-half year deal worth a reported £50,000-a-week.
The Scotland international, whose contract at Rangers was due to run out in the summer, believes Bain was simply "going through the motions" when trying to persuade him to stay in Govan.
"It's not all about money, I loved my time at Rangers and it was great working for Walter Smith," he told the Scottish Sun.
"But I just couldn't have afforded to take the deal they offered me.
"I didn't think I should be taking a pay cut anyway, but it was always going to be tough to sign on the terms offered. As time went on I realised there was no way it was going to happen.
"The club knew that but I think they felt they had to go through the motions of making an offer.
"At one stage in the talks I had with Martin Bain I actually said to him: 'You can't expect me to sign that, can you?' and his reply was 'probably not'.
"The economics just weren't there, there was no way.
"I've moved about in my career and like a challenge, but when you're settled somewhere there's a lot to be said about making that last as long as possible. But it wasn't to be with Rangers."
