The structural diversity and unique physicochemical properties of sulphated polysaccharides of red algae carrageenans (CRGs), to a great extent, determine the wide range of their antiviral properties. This work aimed to compare the antiviral activities of different structural types of CRGs: against herpes simplex virus type 1 (HSV-1) and enterovirus (ECHO-1). We found that CRGs significantly increased the resistance of Vero cells to virus infection (preventive effect), directly affected virus particles (virucidal effect), inhibited the attachment and penetration of virus to cells, and were more effective against HSV-1. CRG1 showed the highest virucidal effect on HSV-1 particles with a selective index (SI) of 100. CRG2 exhibited the highest antiviral activity by inhibiting HSV-1 and ECHO-1 plaque formation, with a SI of 110 and 59, respectively, when it was added before virus infection. CRG2 also significantly reduced the attachment of HSV-1 and ECHO-1 to cells compared to other CRGs. It was shown by molecular docking that tetrasaccharides—CRGs are able to bind with the HSV-1 surface glycoprotein, gD, to prevent virus–cell interactions. The revealed differences in the effect of CRGs on different stages of the lifecycle of the viruses are apparently related to the structural features of the investigated compounds.