It is widely believed that adaptive peripheral neural control circuits and compliant peripheral biomechanics in biological systems are critical for their control of interactions with the environment. Inspired by the sea slug Aplysia californica’s adaptive feeding mechanism, we previously designed a pneumatically actuated soft grasper controlled by Synthetic Nervous Systems for pick and place manipulation. To guarantee the grasping success rate, the controller sends a fixed grasper radius command during grasper closure. However, such a strategy may generate overly high contact force for manipulating soft and fragile objects. To address this problem, we adopted velocity control circuitry to cap the contact force within a force threshold. Furthermore, inspired by the local modulation of Aplysia networks and muscles, we incorporated time-history-dependent control into the grasper controller. Such modulatory mechanisms allow the force threshold to adapt according to the external load. We evaluated the adaptive controller’s performance in simulation and physical hardware. By comparing it with two baselines, we show the grasper can achieve high success rates for pick-and-place tasks and prevent high contact force when manipulating light objects in a simulation environment. Hardware experiments were also performed to demonstrate that the control network could be transferred to the real-world platform. These results support our hypothesis that soft, morphologically intelligent grasping robots with onboard bioinspired adaptation will improve grasping performance.