Compounds simultaneously carrying the monoterpene and coumarin moieties have been tested for cytotoxicity and inhibition of activity against influenza virus A/California/07/09 (H1N1)pdm09. The structure of substituents in the coumarin framework, as well as the structure and the absolute configuration of the monoterpenoid moiety, are shown to significantly influence the anti-influenza activity and cytotoxicity of the compounds under study. The compounds with a bicyclic pinane framework exhibit the highest selectivity indices (the ratios between the cytotoxicity and the active dose). The derivative of (−)-myrtenol 15c, which is characterized by promising activity, low cytotoxicity, and synthetic accessibility, has the greatest potential among this group of compounds. It exhibited the highest activity when added to the infected cell culture at early stages of viral reproduction.