I've noticed many students try to do all the poses no matter what modification you give them, they try to force themselves into the full asana. It is important to understand that yoga is more than the physical workout most people look for in the USA. Yes, it is a fantastic workout, but it can be so much more. There are numerous reports of people "curing" their depression, infertility, insomnia, anxiety, etc through yoga. Those are "cured" by reconnecting to the body, by using the breath and being still. I find it funny, how few people can lie still in the final pose, the "corpse pose". I read a piece of Tibetan literature that stated people can not be still because they have a fear of death. But death is not to be feared and much is to be gained from being still. When you can be still and quiet in the mind and body, there are so many things you can learn about yourself.
So, the next time you "do" yoga, relax into the asanas. If it feels good and you want to stay there longer than the instructor gives you, do it, it's your practice. Also, let yourself go in the final pose. Savasana is about being like a corpse, so give it all you've got! Someone will wake you if you fall asleep, it's okay and it does happen. You just did a fantastic job of being a corpse.