Massive star clusters are observed in galaxies spanning a broad range of luminosities and types, and are assumed to form in dense gas-rich environments. Using a parsec-resolution hydrodynamical simulation of an isolated gas-rich low-mass galaxy, we discuss here the non-linear effects of stellar feedback on the properties of star clusters with a focus on the progenitors of nuclear clusters. Our simulation shows two categories of star clusters: those for which feedback expels gas leftovers associated with their formation sites, and those, in a denser environment, around which feedback fails to totally clear the gas. We confirm that radiation feedback (photoionization and radiative pressure) plays a more important role than Type II supernovae in destroying dense gas structures, and in altering or quenching the subsequent cluster formation. Radiation feedback also disturbs the cluster mass growth, by increasing the internal energy of the gas component to the point at which radiation pressure overcomes the cluster gravity. We discuss how these effects may depend on the local properties of the interstellar medium, and also on the details of the subgrid recipes, which can affect the available cluster gas reservoirs, the evolution of potential nuclear cluster progenitors, and the overall galaxy morphology.