The Algerian centre-back was offered a two-year Ibrox extension while other team-mates Allan McGregor and Steven Davis received lengthy contracts.
Bougherra completed his move to Qatari outfit Lekhwiya last week, although he still has a sour taste in his mouth from his Light Blues spell.
The 28-year-old felt he should have been offered terms in line with his team-mates, rather than staying at the club on the same terms.
"I was in my last year with Rangers and I had choices to make," explained Bougherra. "I either stayed until the end of the season and run out my contract, with the risk that I get injured along the way and find myself without a club next season, or extend my contract at Rangers.
"The proposed extension that Rangers made me had the same financial terms as my present contract - virtually the same pay.
"It wasn't what I was expecting, especially at my age.
"Also, I was offered an extension of two years only, while two or three players at Rangers got five-year contracts. It made me feel sick in my heart."