If this isn't true to a felt degree than it isn't really a sacrifice. King David refused to be given the property that he wanted to build an altar to God on. He wanted to pay for it, desirous of it being a sacrifice. Accompanying the fast is prayer, approaching God. In every single instance that we know of in Scripture when people fast, they pray.
Prayer is vital to the success of the fast, and it is usually geared to a specific request.
Nehemiah asked that God would rebuild the wall of Jerusalem. David asked that his first son of Bathsheba be saved from sickness. Daniel asked that God return his people to his promised land. This seems to be the first reason God's people fast. He places a specific desire in their hearts that drives them to their knees and seek His throne.