The club said they had taken "further disciplinary action" against the defender after Terry decided to accept a four-match ban and £220,000 fine from the FA for racially abusing QPR's Anton Ferdinand.
But Chelsea said they would be keeping their action "confidential" due to club policy.
Lord Herman Ouseley, chairman of Kick It Out, said that stance could damage Chelsea in the eyes of those people who had been waiting many months to see how the club handled the case.
Ouseley told the Press Association: "I believe Chelsea need to be open about the action they have taken. A lot of people will be dissatisfied that Chelsea have not been much more up front about the standards they set and the values they have.
"If they are not prepared to say, it will further damage the trust of those people who still have suspicions about Chelsea's sincerity in dealing with this matter.
"I do welcome what they have said, but they need to be saying more and doing more if they are going to win back the confidence of people who have lost trust in them rather than to sit back and be silent."
Chelsea released a statement on Thursday saying that Terry's language was not acceptable.
The statement said: "The board has taken further disciplinary action in addition to the four-match suspension and £220,000 fine imposed by the FA. In accordance with our long-standing policy, that disciplinary action will remain confidential."
Reading striker Jason Roberts insists he will not wear a 'Kick It Out' T-shirt for the equality group's annual week of action after the racial abuse incidents of the last year.
Roberts claims Kick It Out have not been hardline in their response to the John Terry and Luis Suarez abuse incidents.
The week of action has now started but Roberts told BBC Sport: "I find it hard to wear a T-shirt after what has happened in the last year. I won't wear one.
"I'm totally committed to kicking racism out of football but when there's a movement I feel represents the issue in the way that speaks for me and my colleagues, then I will happily support it.
"I think people feel let down by what used to be called 'Let's Kick Racism Out of Football'. People don't feel like they have been strong enough."
Kick It Out chairman Lord Ouseley said he understood Roberts' feelings.
Ouseley said: "He's not been slow in coming forward about this and I respect his views"
"I can understand his frustrations. If Kick It Out had the power to sort this out then we would have done. Sorry Jason, we don't have that kind of power."
Roberts added that the four-match ban handed to Terry for racially abusing QPR's Anton Ferdinand was too lenient.
He added: "The four-match ban was, for me, not a heavy enough sanction for what happened.
"I'm not happy. Certainly they should have given him a longer ban. The sanction is nowhere near harsh enough."