Baby bottle cleaning question

ma

My daughter is a week old. We bought a bottle/ nipple sterilizer machine. When she’s done with her bottle we usually just rinse it out with water and put it in the sterilizer. I noticed after it’s sterlized there’s some tiny milk spots that are dried. My question is, is it still clean? Or Should I be washing them with soap before sterilizing it? I’m a ftm and freaking out over everything .... thank u