Fat is necessary only to replace the calories lost from not eating carbohydrate. Your protein intake will likely have remained unchanged when you switched to your ketogenic diet, and your energy has to come from somewhere. The good news is twofold: first, unlike carbohydrate, fat has almost no effect on your insulin secretion (apart from the minimum necessary to keep on living), and second, it has over twice the calories, so it takes a lot less fat to provide the same amount of energy.
If you keep your carbohydrate sufficiently low, eat a moderate amount of protein, and fill in with fat till your hunger is satisfied, you will be fine. Don’t restrict calories, because that tells your body to hang on to all its resources until the famine is over. If you eat a ketogenic diet to satiety, your appetite will guide you to the proper amount of food to eat, which will allow you to burn both the fat in your food and the extra fat in your adipose tissue.