Tactile sensing is the current challenge in robotics and object manipulation by machines. The robot’s agile interaction with the environment requires pressure sensors to detect not only location and value, but also touch direction. The paper presents a new, two-layer construction of artificial robotic skin, which allows measuring the location, value, and direction of pressure from external force. The main advantages of the proposed solution are its low cost of implementation based on two FSR (Force Sensitive Resistor) matrices and real-time operation thanks to direction detection using fast matching algorithms. The main contribution is the idea of detecting the pressure direction by determining the shift between the pressure maps of the skin’s upper and lower layers. The pressure map of each layer is treated as an image and registered using a phase correlation (POC–Phase Only Correlation) method. The use of the developed device can be very wide. For example, in the field of cooperative robots, it can lead to the improvement of human machine interfaces and increased security of human–machine cooperation. The proposed construction can help meet the increasing requirements for robots in cooperation with humans, but also enable agile manipulation of objects from their surroundings.