The ability of mammalian cells to deform their membrane relies on the action of the cytoskeleton. In particular, the dynamics of the actin cytoskeleton, assembling at the plasma membrane, plays a crucial role in controlling cell shape. Many proteins are involved to ensure proper growth of the actin network at the cell membrane. The detailed structure of this network regulates the force that is necessary for membrane deformation. We address here how the presence of capping proteins, which limit the length of actin filaments and thus affects network topology, influences membrane shape. We use a system of liposomes, activated to polymerize actin at their surface, and placed in a mixture of purified proteins that reconstitutes actin dynamics. Our system also allows the variation of membrane tension by deflating the liposomes. We show that membrane deformations are clearly favored in the presence of capping proteins in the actin network. Moreover, in the absence of capping proteins, membrane deformations appear only when the liposomes are deflated. Our results unveil that the interplay between membrane tension and actin network structure and dynamics governs cell shape.