Actually your total carb count for the day includes the fiber & is then reduced by the fiber. So, if you're using a site like fitday the carbs listed will include the fiber, which is then listed separately, allowing you to reduce your total carbs by the fiber, leaving you with net carbs.
There is plenty of room in your eating plan for lots of veggies as they give you a lot of bang for your buck. Broccoli, dark salad greens, spinach, kale, etc....