Villa defeated their Midlands rivals 2-0 to book a semi-final spot and a trip to Wembley, but the victory was marred by several instances of home fans invading the Villa Park turf, including one during stoppage time that caused a slight delay to the game.
A large number of fans rushed the pitch again at the final whistle, prompting widespread condemnation and a Football Association investigation.
Villa subsequently issued an apology to West Brom and slammed the actions of those who encroached on the playing surf - a statement that has been noted by West Brom.
However, reports have also emerged that visiting supporters threw seats amid the chaotic scenes and West Brom warned that inappropriate conduct will not be tolerated.
"West Bromwich Albion note the public apology issued by Aston Villa FC in the wake of the disturbing scenes during and after the FA Cup quarter-final at Villa Park," read a statement on the club's website.
"The apology is received in the spirit with which it was intended. The club is also aware of reports of serious misbehaviour involving some of its own supporters.
"It issues an uncompromising reminder today that any supporter found guilty of disorder offences can expect the appropriate sanction from the club. West Bromwich Albion will continue to operate zero tolerance to any fans who bring the club's reputation into disrepute.
"The club also welcomes the FA investigation into the scenes and how they came about; West Bromwich Albion will cooperate fully.
"Pitch invasions cannot be tolerated under any circumstances. The safety of the club's players and staff during and at the end of the game was clearly compromised and that has to be a subject of deep concern for everyone involved."
