Tell them this is just part of "adulting", not in any way a reflection on your parents. It's just part of growing up. Invite them to help set up your apartment if they wish.

My parents didn't want me to get my license. Mom said Dad would be happy to drive me around. I still got my license despite them being nervous and having real reservations about it. Their concerns were very justified even to me. I got my license, bought my own car, etc. My parents saw I could handle it all safely and they were eventually okay.

Your parents may come around given time and them seeing you can handle it okay. You can do this, Aviza! Best of luck!