First of all, I don't think most people who pray actually buy this "genie in a bottle" idea. I think to them praying is more like writing in a diary. "Today was difficult. Give me strength for tomorrow", that sort of thing. This is the impression I get from people when prayer comes up in conversation, they don't think you can ask him for a car and next day you'll have a car. (This would be disastrous for the economy btw.)
So obviously, if you calibrate your requests in such a way that they only ask for "strength" or "courage", ie. quantities that are not measurable, then you set your expectations up not to be disappointed. I also think people who pray actually believe in this "god's will" stuff, so when they don't get what they want they think back to some day when they did get what they wanted, and they tell themselves "perhaps I don't deserve this, perhaps god will grant it if I do something else" etc.
In that regard it's not really slavery, it's more like having a rich and powerful friend who can do favors for you if you make him happy.