Soft grippers, with their inherent compliance and adaptability, show advantages for delicate and versatile manipulation tasks in robotics. This paper presents a novel approach to underactuated control of multiple soft actuators, explicitly focusing on the coordination of soft fingers within a soft gripper. Utilizing a single syringe pump as the actuation mechanism, we address the challenge of coordinating multiple degrees of freedom of a compliant system. The theoretical framework applies concepts from stable inversion theory, adapting them to the unique dynamics of the underactuated soft gripper. Through meticulous mechatronic system design and controller synthesis, we demonstrate the efficacy and applicability of our approach in achieving precise and coordinated manipulation tasks in simulation and experimentation. Our findings not only contribute to the advancement of soft robot control but also offer practical insights into the design and control of underactuated systems for real-world applications.