Yes writing fantasy tends to involve leaps of logic and putting faith in the author, but at its core, that is not what makes a fantasy unbelievable.  That suspension of disbelief must happen in any fiction, whether a mystery, a spy thriller, or when writing fantasy.

The key is primarily to write good characters.  If the dialoge feels forced or the descriptions are unnatural or stilted, then the logci behind the use of magic in the world will quickly become irrelevant.  If the characters act natural and live as organic entities (i.e. stemming naturally from their surroundings, not necessarily made from carbon) within their world then automatically the level of believabilty has increased.

Writing good dialoge will go a long way to make the story believable.  Writing fantasy is not much different from writing fiction of any kind.  The characters must feel as if they belong.  Their actions must correspond to their motives.  Their words must correlate to their actions.  They must react to and interact with each other in a natural manner.  If you accomplish this, then the reasons behind the blood sacrifices required to generate the power necessary to complete the ultimate spell of destruction become less important.  The reasons are still imporant, but now the stage is set so that they can become believeable whereas with poor characters the reader will never even reach this point.

Again, if the characters spring naturally from their world, then the reasons behind the sacrifices and thier reactions to them will already be explained.  If there are flaws in the logic they will generally be exposed already due to the natural tendancies of the characters.  An evil villain predisposed with a hatred for bloodshed would inherently seek an overwhelming, driving motive for a blood sacrifice whereas a bloodthirsty maniac would likely find the power associated with it as an added perk rather than a driving force.  In either instance the logic lies more with the characters than the mechanics behind the world.