On Friday Terry was cleared at Westminster Magistrates' Court of racially abusing QPR's Anton Ferdinand and the FA will now have to decide whether to open disciplinary proceedings under its rules.
It is likely to be at least a week before a decision is made.
The FA can still bring charges even though Terry was found not guilty in court.
Liverpool's Luis Suarez was banned by the FA last season for racially abusing Patrice Evra but that case never went to court.
An FA spokesman said: "The FA notes the decision in the John Terry case and will now seek to conclude its own enquiries. The FA will make no further comment at this time."
Former Manchester United and Tottenham striker Garth Crooks, now a BBC presenter, has criticised the FA for not acting sooner.
Crooks said on www.guardian.co.uk: "The real problem in the Terry case began once the FA failed to take immediate action.
"This lack of fibre by the governing body to act instantly when Terry gave them a statement after the verbal clash with Ferdinand, threw the entire procedure into chaos - forcing everyone associated with the game to either dive for cover or sit on the fence.
"It may have appeared expedient to delay matters at the time but once the police appeared on the scene the FA lost control of the process and the dynamic dramatically changed."
Crooks believes that Terry should still face action from the FA even though the Chelsea player's defence was that he was only repeating what he believed Ferdinand had accused him of saying.
He added: "I believe it was wrong of him to say these words under any circumstances - and though Terry has been found not to have committed a criminal offence, the FA must now decide whether the former England captain should be charged for contravening its own rules.
"If the FA don't act on the undisputed facts, and find Terry guilty of bringing the game into disrepute, a lot of good people are saying to me that there's no point in getting involved in the game at a senior level."
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