"I have a button in my pocket."
Translation:Jag har en knapp i fickan.
Yes, like, if you say in Swedish Jag borstar tänderna ('I am brushing my teeth') we feel that it's quite unnecessary to point out that it's my teeth I'm brushing, since that's the most obvious case. If I'm brushing somebody else's teeth, I'll point that out instead. – The definite form here means that we are speaking about an object that can to some extent be taken for granted ('you know which one I mean').
Since you're the one with the button, then we can safely assume that "the pocket" is your pocket, and not someone else's pocket. If you mean another pocket, then that would be surprising, and we expect you to say so.
It's the same in other languages. In French, we say "I wash myself the hands" to mean "I wash my hands". If I'm washing myself, then whose hands would I wash except mine? :)
You need the indefinite article both in Swedish and English. In both languages, we rarely use the singular without an article, and if we do, it's for more general or abstract things or for instance mass nouns. For typical objects (concrete, countable things) we basically never use them without an article in the singular in either language.