Terry was banned for four matches and fined £220,000 for racially abusing QPR's Anton Ferdinand but some players feel the Chelsea captain escaped lightly - especially compared to Liverpool's Luis Suarez who was banned for eight games following his case involving Patrice Evra.
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 about whether the FA would look again at the tariff for sanctions, Bernstein told a news conference at Wembley Stadium: "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."
Any rule change would have to be proposed by the Football Regulatory Authority and come in from the start of next season.
Bernstein came to the defence of anti-discrimination body Kick It Out after several leading players including the Ferdinand brothers and Reading striker Jason Roberts refused to wear T-shirts backing a week of action at the weekend.
It emerged on Tuesday that talks about setting up a black footballers' association have begun.
Peter Herbert, who chairs the Society of Black Lawyers, said talks about the formation of an organisation - which has a working title of the Black Players' Association - were "at a preliminary stage".
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.
"I have great respect for all the parties, for Anton Ferdinand and Rio Ferdinand. Of course I understand their sensitivities. They have had a pretty rough time. Anton has had a very difficult time as has had his family.
"The fact this thing has taken so long - even though I would justify the process - certainly hasn't helped. I have every sympathy for Anton.
"I'm uncomfortable that people feel uncomfortable, I feel that overall the FA has handled recent issues, not just John Terry, actually very well.
"We support Kick It Out in every respect both morally and financially. I have got to know (Kick It Out chair) Lord Herman Ouseley and he has done fantastically well. He has given me a very hard time even in my first week as chairman, and has been very tough with us but always been very fair."
The FA has been widely criticised for allowing the Terry case to go on for almost a full year - it agreed to delay its hearing until the outcome of a magistrates' court case and Bernstein defended that decision.
He added: "I know the Terry thing took much longer than anyone would want, of course no one would want it to drag on for a year, but there were exceptional circumstances.
"It's easy with hindsight, it was a very particular situation and if it was to happen again and we were asked by the authorities to delay our process for legal reasons would we do it again? Possibly. I certainly wouldn't rule it out, I'm very respectful of the law."
Meanwhile, Professional Footballers' Association chairman Clarke Carlisle believes a breakaway union for black footballers would be divisive and wants to meet the Ferdinand brothers and Roberts to discuss their aims.
Carlisle said: "I've had a number of conversations with Jason over the past few months. The most recent of them was on Sunday and they will continue.
"Jason explained one or two things to me but I don't know what the full intentions or the requests are of this breakaway group.
"The threat is very real because the proposal is there and the discussions have been had so it's obviously something that has been mooted within the industry.
"We have been having meetings with Jason and we have desperately been trying to get Rio into the meetings and that will continue."
Gordon Taylor, chief executive of the PFA, called for unity.
He told the Daily Telegraph: "If they want their own particular select group who they feel can influence everybody more than the whole PFA as a union together, I would say they are seriously mistaken.
"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."