If you took your driving test but had doubts about your abilities, would you still be able to drive okay? The same applies to magic, you need to firmly believe in what your doing otherwise its just a pointless exercise.
Belief in the spell or belief in a god? You need a belief in both, especially the spell since not all spells call on a specific god. If you are casting a spell that calls on Oden and you don't follow Norse mythology at all, you shouldn't call on him. There are other factors too like energy and visualizing, but belief is key. If the spell calls on a god you don't work with or believe in, I would either omit the god in question, or substitute it with a similar god I worked with.