This paper presents a conceptual design and implementation of a soft, compliant 3D printed gripper (SurgGrip), conceived for automated grasping of various surgery-based thin-flat instruments. The proposed solution includes (1) a gripper with a resilient mechanism to increase safety and better adaptation to the unstructured environment; (2) flat fingertips with mortise and tenon joint to facilitate pinching and enveloping based grasping of thin and random shape tools; (3) a soft pad on the fingertips to enable the high surface area to maintain stable grasping of the surgical instruments; (4) a four-bar linkage with a leadscrew mechanism to provide a precise finger movement; (5) enable automated manipulation of surgical tools using computer vision. Our gripper model is designed and fabricated by integrating soft and rigid components through a hybrid approach. The SurgGrip shows passive adaptation through inherent compliance of linear and torsional spring. The four-bar linkage mechanism controlled by a motor-leadscrew-nut drive provides precise gripper opening and closing movements. The experimental results show that the SurgGrip can detect, segment through a camera, and grasp surgical instruments (maximum 606.73 gs), with a 67% success rate (grasped 10 out of 12 selected tools) at 3.21 mm/s grasping speed and 15.81 s object grasping time autonomously. Besides, we demonstrated the pick and place abilities of SurgGrip on flat and nonflat surfaces in real-time. The online version contains supplementary material available at 10.1007/s11012-022-01594-6.