Using a low-temperature scanning tunneling microscope, we have investigated the Abrikosov vortex lattice and its electronic structure on 2H-Nb₁₋ₓTaₓSe₂ single crystals for a range of Ta substitutions from x=0.00 to x=0.20 and with the magnetic field perpendicular to the basal plane. The material properties and in particular the electronic mean free path of 2H-Nb₁₋ₓTaₓSe₂ can be modified in a systematic manner by varying the Ta concentration. For all Ta substitutions considered, we show that the vortex lattice is aligned with the underlying atomic lattice. We find that the zero-bias conductance peak observed in the vortex core is strongly reduced both in intensity and spatial extent as x increases to 0.15, and vanishes when the Ta concentration reaches x=0.20. These results show for the first time the progressive destruction of the vortex core conductance peak with increasing disorder in a type-II superconductor.