Rio Ferdinand was struck by a coin thrown from the crowd as Manchester United celebrated Robin van Persie's deflected last-minute winner, while only the intervention of City keeper Joe Hart prevented another fan confronting the defender.
And Bernstein told Sky Sports News: "It is deplorable to see those incidents and to see Rio Ferdinand with blood on his face is absolutely terrible."
He continued: "I think it's disturbing that we're seeing a recurrence of these types of incidents. We've had racial abuse issues, the odd pitch incursion, things being thrown at players - it's very unacceptable and has to be dealt with severely."
Bernstein promised tough action from the FA to try to stamp out the chances of further incidents occurring.
"It's very disappointing: so much of football is so good, great things are happening in football as a whole, but these odd incidents get the headlines - and understandably because they are serious matters, they are unforgivable things," he added.
"When you think of the millions watching football every week, or involved in football, to see it hijacked by these incidents is awful so we have to deal with it in the strongest way we can.
"It's a difficult social problem. I think there's a copycat thing: something happens and other people copy it and this sort of thing can spiral. To my mind it's for the FA, the whole game of football and the authorities to work together to deal with this most severe matter.
"I believe that if necessary these people need to go to the court and be banned for life, if they're found out.
"It's important that matters are brought to a head and people understand that there is no room for this in football at all, and we'll do everything we can within the FA. I know the rest of football feels the same, it's a blot on the game."
Source: PA
Source: PA