I am a working single parent and cannot fulfill the roles of both parents. I sense my child feels a vacuum when she sees the fathers of other kids doing things with them. How can I make up?

Do not try to be the father and the mother of your child. It is not possible. Talk to the child and make them understand that there are the two of you and you need to work together to make the best of it. As long as your child understands and sees you doing your best, they will not blame you for being unable to do certain things because of the absence of a second parent.