There were ugly scenes towards the end of Villa's 2-1 win on Sunday when Ollie Watkins put the visitors ahead in the 85th minute and celebrated in front of his former club's fans.
Villa midfielder Boubacar Kamara was sent off in injury time for violent conduct following a scuffle involving several players.
Both clubs have been charged with failing to ensure their players and staff did not behave in an improper and/or provocative way and have until Friday to respond.
Keane Lewis-Potter opened the scoring for London club Brentford on the stroke of half-time.
But the game changed when Brentford defender Ben Mee was sent off about 20 minutes from time after flying into Leon Bailey.
Alex Moreno levelled in the 77th minute, with Watkins completing the turnaround eight minutes later.
After the match, Villa manager Unai Emery said he would take action to tackle the indiscipline.
"At the end some moments, some behaviour, of us as well, I'm going to manage our behaviour and take control of it," he told the BBC. "I will analyse it with our players because it was not normal.
"We were a bit excited and we needed control of ourselves. When you are reacting like that, other players and the other opponent is maybe not being in good behaviour like the match needed."
Emery added: "I'm going to manage everything we did that was not good and our mistakes in our behaviour."
Third-placed Villa sit one point behind Premier League leaders Arsenal.
