When robotic manipulators perform high-level tasks in the presence of another agent, e.g., a human, they must have a strategy that considers possible interferences in order to guarantee task completion and efficient resource usage. One approach to generate such strategies is called reactive synthesis. Reactive synthesis requires an abstraction, which is a discrete structure that captures the domain in which the robot and other agents operate. Existing works discuss the construction of abstractions for mobile robots through space decomposition; however, they cannot be applied to manipulation domains due to the curse of dimensionality caused by the manipulator and the objects. In this work, we present the first algorithm for automatic abstraction construction for reactive synthesis of manipulation tasks. We focus on tasks that involve picking and placing objects with possible extensions to other types of actions. The abstraction also provides an upper bound on path-based costs for robot actions. We combine this abstraction algorithm with our reactive synthesis planner to construct correct-by-construction plans. We demonstrate the power of the framework on a UR5 robot, completing complex tasks in face of interferences by a human.