Modern western (i.e. American) culture has placed a tremendous emphasis on the importance of individual independence. I've been following a related train of thought, lately, and the proverb "Give a man a fish and feed him for a day; teach a man to fish and feed him for the rest of his life," is applicable. The proverb proposes a false reality where fish is the only thing to eat and fishing is the only productive work. It ignores the diversity and interdependence that exists in real society. At its most basic level, that interdependence exists as a barter system: I give a man a fish and he gives me some corn and we both eat.
Somehow I've translated philosophy into economics... But the example illustrates the point: dependence is not bad, and for all the emphasis we put on independence, it is a false ideal (and probably an illusion in itself).
In other words, Andrew Cheong is very correct in his answer - belief (or confidence) in one's self and belief in a higher power are not mutually exclusive. Belief in and dependence upon a higher power can only be bad if the belief produces negative results.
Can a lack of self confidence be a negative result of belief in God?
Again, only if that lack of self confidence actually has tangible negative consequences to the individual. I know a lot of people who have no self confidence whatsoever who still live fairly happy and productive lives. I also know a lot of people who have a great deal of faith and confidence in God, but who also have a great deal of confidence in themselves. My own observations lead me to conclude that faith (which is different from mere belief) in a God typically results in greater personal happiness and success.