The belief in self is the biggest asset your child can have at this stage and even later in life. You can inculcate personal responsibility in your child in many ways. One effective way is through implementation of daily chores.
What you can do
You can start with your child's room. By cleaning his own room, your child is learning self-reliance and how to take care of himself. One or two tasks a day like making the bed, picking up toys is sufficient for your child to begin with. Take some time to demonstrate how the task has to be done. Once he does it on his own, praise him for his efforts and your child will be motivated to do even better next time. If he is reluctant to do the task, you can encourage him by saying, “Rewards are obvious. You will get to spend time in a clean room where all things are kept in order and easy to find."
Another strategy to get your child excited about doing his chores is to maintain a kid's chore chart. These can include making the bed, hanging up the backpack, putting shoes away, putting away folded laundry etc. Once your child accomplishes a task, ensure he puts a check mark on the chores chart. At the end of each week, it’s encouraging to see the tasks that were accomplished. He will also learn to manage his time better if any chore was not done.
With clear expectations, genuine praise and consistently implementing chores, your child will learn to be responsible and independent in future.