Was your baby bunny with its mother, or had they been seperated? Ideally, a baby bunny needs to remain with its mother until it is 6-8 weeks old. If it was weaned earlier than this, it may have died because it still needed its mother's milk.
Baby rabbits are born blind and hairless. Their mother makes a nest with straw and her own hair for them to live in. She will not stay in the nest with them, but will quickly visit the nest only 1-2 times per day to nurse them.
They begin to grow fur right away, and by a week old you can tell what color they are. Their eyes begin to open between 12-14 days old. At around 3 weeks old they start to come out of the nest and may start to nibble on their mom's food, but they still need their mother's milk.
Young rabbits at 6-8 weeks can be weaned from their mother. They should be fed good quality commercially made rabbit pellets, which have alfalfa, grains, and necessary vitamins and minerals in them. They also need access to fresh clean water all the time. They do not need treats, but if you do feed treats, do not feed watery vegetables like lettuce, as this could give the rabbit diarreah.
For a medium sized rabbit, their cage should be at least 24" x 24". One with a wire floor, where the droppings fall through, are best for the rabbit. You can simply clean the tray under the cage every few days without disturbing the rabbit. They do not need to be walked, but might enjoy playing outside of their cage. Be sure to supervise them when out of the cage, as they love to chew on things and could get hurt chewing on wires or other dangerous things.
Rabbits need to be kept out of direct heat-- if they are housed outside, always have a shady cool spot for them in the summer. In the winter they can tolerate cold if they have a sheltered box and straw in their cage, and fresh unfrozen water to drink.
Rabbits are a fun quiet pet that are easier to keep than some other pets, but they still require some basic care. There are books available on rabbit care, and also some information available through online searches.If well cared for, a rabbit can live until 5-10 years old.
I am sorry your rabbit died. It may not have been anything you did wrong-- sometimes a rabbit will die and you will not see any symptoms or signs of trouble at all. Good luck if you decide to try rabbits as a pet again.