In English, there are three words spirit, mind and soul to express beings which transcend body. To my understanding, spirit is for faith, morality and worship, mind is for reason, ethics and knowledge, and soul is for emotion, law and behavior. Spirit transcends mind and shines lights in mind, and mind transcends soul and shines lights in soul. So, your spirit is the most top of you.
For God is spirit, directly "worship in spirit" means worship in God. This is very correct, but practically you should do something more, that is you should prepare yourself well enough to make sure you are on your most top with your own spirit, upon your whole mind which in turn upon you whole soul.