Reverend Canon Gavin Ashenden stepped down as one of the monarch's 33 chaplains in order to have more freedom to "speak out on behalf of the faith", following discussions with Buckingham Palace.
The controversy centres on an interfaith service held at St Mary's Episcopal Cathedral over the Christmas period, where a chapter from the Islamic text was read out.
The chosen verses tell the story of Christ's birth, but claim he was not the son of God and should not be worshipped as such.
The reading sparked widespread outrage amongst the Christian community, and Police Scotland is currently investigating a series of abusive messages directed at the cathedral on social media.
Rev Gavin Ashenden has quit as one of the Queen's Chaplains over the Koran reading
Speaking to Radio 4's Sunday programme, Reverend Ashenden said: "The problem with what happened in Glasgow was that although it was presented as a way of building bridges and a way of educating people, it was done badly in the wrong way, in the wrong place, in the wrong context.
"There are number of members of the congregation who have written open letters complaining of the profound upset they experienced as people of the Eucharistic community who had come to worship Christ.
"So to have a reading from the Koran at that point was a fairly serious error for the Christian worshipping community.
"But to choose the reading they chose doubled the error. Of all the passages you might have read likely to cause offence that was one of the most problematic."
Of all the passages you might have read likely to cause offence that was one of the most problematic
Rev Gavin Ashenden
He announced his resignation on his blog, ahead of an the programme's broadcast.
"After a conversation instigated by officials at Buckingham Palace, I decided the most honourable course of action was to resign," Reverend Ashenden wrote.
"I have held the position for the last nine years. But over the last few years people who objected to my defending the Christian faith in public wrote to both Lambeth Palace and Buckingham Palace to try to get the association ended.
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"When I was confronted with these attempts to silence or defenestrate me, my reaction was to ask 'in what way is a priest defending the faith on behalf of a monarch who was Defender of the Faith, incongruous or improper?'
“I have come to see that the situation is more complex than that."
The Koran celebrates Jesus as a profit, but not the Son of God
Reverend Ashenden said it was "wrongly assumed" that as a Queen's Chaplain he had "the Queen's ear" and that by expressing his own views there was a danger they would be construed by the media as those of her Majesty.
"There is a very important convention that the Queen should not be drawn into public affairs where she is deemed to be taking a position,” he wrote.
“She needs to be above ‘positions.’ That is how the monarchy rides out political turbulence.”
He concluded: "Because I think it a higher and more compelling duty to speak out on behalf of the faith, than to retain a public honour which precludes me doing so at this time, I resigned my post."
St Mary's Episcopal Cathedral has come under fire for the reading
Reverend Ashenden had previously criticised the reading in a letter to The Times.
He has also spoken out about certain passages in the Koran before.
In 2015, he appeared on Iain Dale's LBC radio show and said there were "over 100 verses inviting people to violence" within the text.
The provost of St Mary's Cathedral, the Very Rev Kelvin Holdsworth, previously defended the Koran reading as a way of "deepening friendships locally”, although he declined to comment when asked by the BBC if he was aware of the content of the passage before it was read out.
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