Magnetic excitations of the effective spin S=1/2 dimerized magnet Ba_{2}CoSi_{2}O_{6}Cl_{2} have been probed directly via inelastic neutron scattering experiments at temperatures down to 4 K. We observed five types of excitation at 4.8, 5.8, 6.6, 11.4, and 14.0 meV, which are all dispersionless within the resolution limits. The scattering intensities of the three low-lying excitations were found to exhibit different Q dependencies. Detailed analysis has demonstrated that Ba_{2}CoSi_{2}O_{6}Cl_{2} is a two-dimensional spin dimer system described only by a single dimer site, where the triplet excitations are localized owing to the almost perfect frustration of the interdimer exchange interactions and the undimerized spins, even in small concentration, make an essential contribution to the excitation spectrum.