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.
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.
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 England in which, unfortunately, the reputation of English football has been damaged.
"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 on Thursday 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."
There has also been criticism from black players of the Kick It Out campaign, with Reading's Jason Roberts leading players stating they will not wear organisation's T-shirts during their current "Weeks of Action" as it has not been hardline in its response to the Terry and Luis Suarez abuse incidents.
Suarez was hit with an eight-match ban last season for racially abusing Manchester United's Patrice Evra, with Bernstein noting: "Many have highlighted the difference between this sanction (for Terry) and the eight matches imposed on Luis Suarez.
"In the case of Suarez, however, the commission found that repetition of the insulting language used was a further aggravating factor."
He also defended Kick It Out, saying: "This coming fortnight's 'Kick It Out' campaign is a valuable reminder of the strength of the game when addressing these issues together, and it is this positivity that our game must harness.
"I hope this time next year when we are marking 20 years of the 'Let's Kick Racism Out of Football' message we will be reflecting once again on the positive power of football to publicly oppose all forms of discrimination and ensure our sport is inclusive to all."
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