Yes, blackberries can be grown in containers. You can read more about berry container planting here: https://www.gardeningknowhow.com/edible/fruits/berries/berries-growing-container.htm
There could be a number of reasons that your seedling plants disappeared besides insects. They could have been eaten by rabbits/deer or the seedlings could have shriveled up and died (damping off disease possibly due to over-watering).
For more information on growing blackberries, please visit the following link: