Terry was suspended for four games and fined ?220,000 by an independent Football Association regulatory commission after he was found guilty of racially abusing QPR defender Anton Ferdinand in a game last season.
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 England in which, unfortunately, the reputation of English football has been damaged."
The time taken for the FA to handle the case has been criticised, although their 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 Thursday's deadline.
Bernstein continued: "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 Independent Regulatory Commission as to how matters could and should be improved. I will ensure any lessons that arise from the ruling will be learnt quickly and appropriately.
"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."
England's Under-21 team, and in particular full-back Danny Rose, suffered abuse in Serbia on Tuesday while Lazio were fined £32,500 by UEFA for monkey chants by their fans during a Europa League tie against Tottenham.
Bernstein continued: "No player should suffer the intolerable abuse the likes of which Danny Rose was subjected to in Serbia."
Source: PA
Source: PA