"To think about problems or unpleasant things that make you anxious or to make someone feel anxious." This is how Cambridge Dictionaries Online defines the word, "worry." The key word here is not about to think about problems and unpleasant things, but about to feel anxious. We certainly cannot avoid, or more likely should not avoid thinking about problems and unpleasant things, because it is an important part of our spiritual cultivation that we process our problems and unpleasant things properly and appropriately. Yet, as Jesus emphasizes, we should do it without being anxious.
(References: Genesis 2:18)