Plitidepsin is a safe antiviral for COVID-19 patients that impairs SARS-CoV-2 replication by targeting host factors implicated in protein translation. Here we used deep quantitative proteomics coupled to infectious assays and transmission electron microscopy to dissect its antiviral activity. Plitidepsin inhibited the synthesis of all SARS-CoV-2 proteins, including R1AB required for double membrane vesicle formation needed for viral replication. Yet, less than 14% of the cellular proteome was affected by plitidepsin, which up-regulated translation factors such as eIF4A2 and eIF2S3 and ribosomal proteins associated to protein biosynthesis. At a concentration of 50nM, plitidepsin resulted in a compensatory proteostasis that rescued protein translation. Moreover, plitidepsin inhibited other RNA-dependent and non-integrated DNA viruses from the Flaviviridae, Pneumoviridae, and Herpesviridae families, but failed to block DNA-integrated proviruses from the Retroviridae family. Unraveling the mechanism of action of host-directed therapies like plitidepsin is essential to develop broad-spectrum antivirals ready to deploy when future pandemics begin.