Nicola Nugent said the device was put through the letterbox of her home on Stanhope Street at about 03:00 BST on Friday. It exploded, setting off the fire alarm and causing damage to the front door and the hallway.
Ms Nugent and her four children escaped from the home and no-one was injured. She told BBC News NI she remains in shock.
Photographs from the scene show a bomb disposal robot beside a wheelie bin outside the red-brick terrace, with a police car also present.
The family said they believe the attack was a case of mistaken identity. Police have not yet said who they believe was responsible.