It depends on how and how long they are cooked.
Vegetables are filled with water-soluble nutrients. Meaning, the more they cook, the more these nutrients are cooked out of the veggies. So ways to keep your veggies healthier...
1. Don't steam them or boil them in water if you can avoid it.
2. Instead, cook them in a dash of cooking spray, or a little pat of butter.
3. Microwave them! This is actually the "healthiest" form of cooking your veggies because it is the fastest and doesn't give the nutrients much time to escape.
4. If cooked vegetables is your only form of this food group, then focus on the vegetables that have more to offer (like broccoli, carrots, tomatoes). Ironically, some vegetables offer other benefits when cooked (carrots, for instance, only have beta-carotene when boiled).
I think you'll be fine, but consider a supplement that provides some of the same vitamins and minerals, and eat a colorful salad every once in awhile!