Perhaps you're not being clear.
Perhaps I am not. Try this.
Science is a methodology. It is perhaps the most important one humans have ever developed, in terms of the gaining of knowledge and real-world effects. But it is limited. By its very definition, science done properly:
1. Can only examine testable propositions.
2. Can only examine natural phenomena, and can only test natural explanations for said phenomena.
3. Can only falsify, never verify, an explanation.
Large avenues of human thought are removed entirely from the realm of science by #1. Ethics, philosophy and religion are the big ones. Now, that's not to say that ethics, philosophy and religion can't be studied scientifically. They can. But science can only examine them descriptively. There is no way to test a prescription. Even if you use science to make an argument in these fields (e.g., arguing that it is morally wrong to harm apes on account of scientific evidence they are self aware), you are using scientific knowledge, but making a non-scientific argument.
#2 follows from #1. Supernatural events are, by definition, not testable, so science cannot even consider them. All scientific theories are inherently naturalistic, but that's not because science has examined other explanations and rejected them. It is because science
by definition cannot consider non-natural theories, as the methods of science are wholly unsuited to studying them. Imagine for the sake of argument that you personally witnessed a miracle. No matter how sure you would be of what you saw, science would never back you up. Even if you recorded the miracle on video. Even if you had 3,000 fellow eye witnesses. All of these things would seem to strengthen your argument that the miracle really did happen, but they would all be irrelevant to science. Science would simply say, "We can't test that," and move on.
#3 is somewhat ironic, since people often think of science in terms of facts. But, while scientists can verify facts (e.g., the existence of a particular fossil), it can never verify an explanation (e.g., common descent through natural selection). Instead, science simply allows us to identify the best explanation we have. Certain scientific theories, like evolution, are so well-backed that it's ridiculous to withhold our tentative assent, but tentative it always is. It is at least theoretically possible that someone will discover a genuine fossil of a human in Jurassic bedrock, and the entire theory will fall apart.
Because science is limited in these ways, other forms of knowing can fill in the gaps. If we want to discuss the existence of God, we use logic and philosophy. Science will not help us. When you limit what you allow your brain to consider only that which you get from science, you are cutting your mind off from all sorts of potentially rewarding intellectual exercises.