This is true for many vegetables, but not all. The nutrients found in carrots are actually more digestable and easily absorbed if they are cooked. It really depends on what nutrient you are talking about. For example, vitamin C is easily destroyed by heat while vitamin E is not. Here's an easy-to-read article about how the nutritional value of food changes with heating, canning, frying, etc:
http://www.saskschools.ca/curr_conte.../keepnutr.html