Villa booked their spot in the semi-finals of the competition courtesy of a 2-0 victory against their Midlands rivals, with Fabian Delph and Scott Sinclair on target.
Sinclair sealed the win for Villa five minutes from the end, which promoted dozens of supporters onto the field to join in the goal celebrations.
More fans returned to the pitch during stoppage time before the final whistle sparked a mass invasion and Villa have moved quick to condemn the chaotic scenes, which could have serious repercussions.
"The club does not condone supporters invading the field of play under any circumstances," the statement read.
"We are very disappointed that what should have been a very memorable and proud moment for our fans was marred by the actions of those who could not control themselves.
"They have let both themselves and their club down.
"The club extends its sincere apologies to the Football Association, the West Bromwich Albion directors, manager Tony Pulis and all his staff and players."
