In reality, you do burn a higher proportion of calories from fat during low-intensity exercise...but, you burn more total calories during high-intensity exercise and it's the total calories that matter when it comes to weight loss, not the percentage of fat or carbs used.
Does that mean you shouldn't do low-intensity exercise? Not at all. You can still burn calories, although you may need to workout longer to burn the same number of calories as high intensity exercise. Both high and low intensity exercises have a purpose and having a variety of workouts with different levels of intensity is a great way to challenge different energy systems in your body and train different aspects of your health and fitness.
And, remember, losing weight is also a function of what you're eating so tracking your calories and making sure you're eating less than your burning is another way to ensure you're losing fat.
For more, check out The Truth About the Fat Burning Zone.

