Terry decided this week not to appeal the decision, leaving Chelsea to decide what action of their own to take.
Buck said on talkSPORT: "John will continue to be captain of the club. We have taken disciplinary action and we think it is firm disciplinary action and appropriate for the circumstances.
"We have kept in mind first of all that a court of criminal law found him not guilty. Of course we also note the FA decision and we certainly respect that decision. We've kept these factors in mind, we've consulted with the owner Mr Abramovich.
"This is not a decision we've taken lightly, it's not a decision we took in a half-hour meeting, we discussed it over a long period of time and we think we've taken appropriate disciplinary action."