Terry was suspended for four games and fined £220,000 ($341,000) by an independent
The time taken for the FA to handle the case has been criticised, although its investigation was held up by the need to defer to the police and the Crown Prosecution Service's criminal proceedings.
The governing body's verdict was finally announced two weeks ago and Terry accepted the sanction ahead of this week's deadline.
And a statement from Bernstein on the FA's website read: "The decision by John Terry not to appeal his FA charge hopefully brings to a close a difficult period for the domestic game in
"John Terry has now been sanctioned and held accountable for his actions. I am pleased he has apologised and we must now draw a line under this matter.
"We too will learn from the case. We have noted criticisms made by the
"It is a shame that one high-profile incident has had such a major impact. The damage of this affair is not irreparable, but as events this week have shown there are still many lessons to be learnt in the wider fight against racial abuse and discrimination of all types."
Liverpool manager Brendan Rodgers has spoken of his relief after his son Anton was cleared in a sex case involving a teenage girl.