Recently, suction-based robotic systems with microscopic features or active suction components have been proposed to grip rough and irregular surfaces. However, sophisticated fabrication methods or complex control systems are required for such systems, and robust attachment to rough real-world surfaces still remains a grand challenge. Here, we propose a fully soft robotic gripper, where a flat elastic membrane is used to conform and contact parts or surfaces well, where an internal negative pressure exerted on the air-sealed membrane induces the suction-based gripping. 3D printing in combination with soft molding techniques enable the fabrication of the soft gripper. Robust attachment to complex 3D and rough surfaces is enabled by the surface-conformable soft flat membrane, which generates strong and robust suction at the contact interface. Such robust attachment to rough and irregular surfaces enables manipulation of a broad range of real-world objects, such as an egg, lime, and foiled package, without any physical damage. Compared to the conventional suction cup designs, the proposed suction gripper design shows a four-fold increase in gripping performance on rough surfaces. Furthermore, the structural and material simplicity of the proposed gripper architecture facilitates its system-level integration with other soft robotic peripherals, which can enable broader impact in diverse fields, such as digital manufacturing, robotic manipulation, and medical gripping applications.