"When I was little I did not have a mobile phone."
Translation:Когда я был маленький, у меня не было мобильного телефона.
У меня не было мобильного телефона could be translated literally as "There was no mobile phone at my side". Neither "I" nor "phone" is a subject of this sentence (at least in Russian); rather, it has no subject, so a neuter gender is used. Another example of a sentence without a subject: Темнело. - It was getting dark.