Jesus reminds us that prayer is a little like children coming to their parents. Our children come to us with the craziest requests at times! Often we are grieved by the meanness and selfishness in their requests, but we would be all the more grieved if they never came to us even with their meanness and selfishness. We are simply glad that they do come--mixed emotions and all.
This is precisely how it is with prayer. We will never have pure enough motives, or be good enough, or know enough in order to pray rightly. We simply must set all these things aside and begin praying. In fact, it is in the very act of prayer itself--the intimate, ongoing interaction with God--that these matters are cared for in due time.
What I am trying to say is that God receives us just as we are and accepts our prayers just as they are. [excerpt from Richard Foster's book Prayer Finding The Heart's True Home]