The 69-year-old has urged Manchester City to set an example by banning troublemakers after violence broke out following Sunday's controversial game at the Etihad Stadium
Manchester United defender Rio Ferdinand was struck by a coin from the crowd and later confronted by a fan after the Red Devils sealed a 3-2 win at the home of their local rivals.
And Bernstein has called for those involved to be investigated, vowing to use the FA's powers to support any action taken.
He told Sky Sports News: "What's happened is totally unacceptable, deplorable. To see Rio Ferdinand with blood on his face is absolutely terrible.
"It's sad to see such a fantastic match followed by headlines.
"It's disturbing that we're seeing a recurrence of these sorts of incidents. We've had some racial abuse incidents, pitch incursions, things being thrown at players.
"It's very unacceptable. It's for the FA, the whole game of football, the authorities to work together and deal with it in a most severe manner - going to court to get life bans for these people.
"It's a social problem, a case of copycat, so it's important to bring matters to a head. We will do everything we can to stop this blot on the game."