Not sure I understand what you mean by a "sacrifice" to worship someone.
Worship, properly so called, requires something be "offered up" to the object of devotion. It could be anything from incense (as in the cult of Roman Emperor worship) to a human being... or even a divine Person (as in the worship of Almighty God).
Adoration, for instance, requires that the object of devotion be acknowledged to be the source of his/her own power, authority, beauty, etc.. So Almighty God may be adored but the BVM may not be adored because she is the not the source of her attributes.