The defender is fighting a misconduct charge that was brought despite being cleared in court of racially abusing Queens Park Rangers defender Anton Ferdinand during a Premier League match last October.
The 31-year-old Terry decided Sunday night that his position with England had been made "untenable" by the FA's decision to pursue a case, although he had been allowed to keep playing despite being stripped of the captaincy before the trial.
"I don't see how we've made (his position) untenable; they're two very separate processes," FA General Secretary Alex Horne responded Monday at Wembley Stadium, where an independent four-man FA panel is hearing the case.
Hodgson withstood widespread criticism to take Terry to the European Championship in June only weeks before the criminal trial, but he will now be without a key defender for the rest of 2014 World Cup qualifying and beyond.
"I'd like to thank John Terry for his commitment to the England team since I became manager," Hodgson said in a statement. "I am of course disappointed to lose a player of John's international experience and exceptional ability.
"I have enjoyed a good relationship with John during my time as England manager and I reluctantly accept his decision."
Hodgson was appointed England coach because Fabio Capello quit in February following the decision by the FA to strip Terry of the captaincy.
A magistrate in July cleared Terry of a racially aggravated public order offence despite describing the player's defence as being "under the cold light of forensic examination, unlikely."
Terry did not deny using an offensive term during the west London Premier League derby at QPR last October but said all he did was sarcastically repeat the words he is accused of using.
"I've been called a lot of things in my football career, and outside of football as well, but being a racist is not one I'm prepared to take at all ... I'm not having anyone — let alone Anton — think that at all about me because that's not in my character at all," Terry said during his initial interview with FA investigators that was heard in court.
Ferdinand said he had been goading Terry about his alleged extramarital affair with the former girlfriend of ex-England teammate Wayne Bridge.
Despite Ferdinand being described as a "believable witness," the magistrate decided that Terry couldn't be convicted because the prosecution could not prove he was lying.
There is a lower burden of proof for the FA charge, however, so Terry could be found guilty on the "balance of probabilities" that he "used abusive and-or insulting words and/or behaviour ... (and) included a reference to the ethnic origin and-or colour and/or race of Anton Ferdinand."
Liverpool striker Luis Suarez was banned for eight matches last year for racially abusing Manchester United defender Patrice Evra in a Premier League match.
Significantly, the FA disciplinary panel formed for that case ruled that the context of Suarez's use of a racial slur was not relevant, concluding: "It does not depend on whether the alleged offender intended his words to be abusive or insulting."
The FA has already imposed one punishment for racist abuse in connection with the case.
Anton Ferdinand's brother Rio was fined 45,000 pounds ($73,000) in August after being found guilty of improper conduct following a Twitter gibe about Chelsea defender Ashley Cole, who gave evidence in court defending Terry.
Ferdinand was found guilty of referencing ethic origin and race when he endorsed a tweet that referred to Cole as a "choc ice," a slang term perceived as meaning black on the outside and white on the inside.
Terry's FA hearing is expected to last at least three days, with a no date set yet for the verdict. Both Terry and Anton Ferdinand were in attendance Monday.
By already opting to end his England career after 78 appearances across nine years, Terry has prevented the FA from having to ban him from representing his country again in the event of a guilty verdict.
Terry has been at the centre of controversy surrounding the England team for the past two years.
England's preparations for the 2010 World Cup were plunged into turmoil after Capello fired Terry as captain when the affair allegations — referenced by Anton Ferdinand — first emerged and led to Bridge retiring from international football.
The centre back was reinstated in March 2011 but was stripped of the captaincy for a second time in February, overshadowing England's buildup to another major tournament.
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