Any process in which a virus stops, prevents, or reduces the activity of the host TAP complex, a heterodimer composed of the subunits TAP1 and TAP2 (transporter associated with antigen presentation). The TAP complex functions in the transport of antigenic peptides from the cytosol to the lumen of the endoplasmic reticulum, where they are loaded onto the MHC class I. By inhibiting the TAP complex, the virus prevents viral particles being presented at the cell surface, and thus evades the host immune response.