Carrots need to be in big pieces because of the long cooking time. They still won't have much bite left but you can squash them into the gravy with your fork. You could always just put them in for the last half-hour or so but I can't be arsed with that. The best way to cook carrots as a veg is to roast them in the oven for about 25 minutes in fairly big batons in seasoned fat. Some lemon thyme scattered in with them is good. They end up far from inedible. Good for you too.