Bernstein's call came on the same day it was revealed discussions about the formation of a black players' association had begun.
According to Herbert, the proposed
Terry was banned for four matches and fined £220,000 ($341,015) for racially abusing Queens Park Rangers'
Last week also saw some England Under-21 players complain of abuse in Serbia.
There is no fixed sanction for racism under FA rules, independent disciplinary commissioners work on the basis of doubling sanctions if there is an "aggravating factor" such as racial abuse.
Asked whether the FA would look again at the tariff for sanctions, Bernstein said: "It's on the agenda to look at it again.
"The FA received a certain, probably limited degree of criticism for its processes in the Terry thing. We will look at that.
"I think the tariffs will need looking at but given the existing scenarios and given other punishments elsewhere actually the commission got it pretty much right."
However, a great deal of damage has already been done and some players want the agenda to be more hard-hitting than the Kick It Out campaign, which has commanded attention following the decision of a number of players not to wear their T-shirts at the weekend.
Herbert told Press Association Sport that a new body "would be a bit more radical (than Kick It Out)".
Herbert added: "The fact we are having this conversation (shows) the campaign has not achieved what it should have achieved.
"It's no criticism of what they've done, we work with them, we know the people involved but it needs to be taken to the next level.
"I think the incidents such as happened in Serbia, they need to rattle a few cages in the Serbian government and that is not going to be happening at the moment.
"UEFA has given a derisory fine for these incidents (in the past).
"Things like that have got us to a place where we are aware that many black players and people in the industry are seriously unhappy and are quite angry and frustrated and disgusted by what is going on and there has to be a new way of doing things."
Bernstein came to the defence of anti-discrimination body Kick It Out after several leading players, including
Bernstein said: "Do I hope players will stay within Kick It Out? Yes I do.
"Fragmentation would be a shame, but at the same time we have to understand on moral issues people have to be able to make their own choices but I hope it doesn't lead to a fragmentation, in the interests of everybody."
He said: "If we are not careful this will set us back years. It would not only set back the game, it would set back the anti-racist initiative. It would encourage the extremists."
English Premier League
Shakhtar Donetsk chief executive Sergei Palkin claims there has been no approach from Liverpool for in-demand midfielder Henrikh Mkhitaryan - but it would be willing to listen to offers.