The Church of England's Rev Gavin Ashdenden told Radio 4 reciting a passage of the Islamic holy book during an Epiphany service at St Mary's Cathedral caused "serious offence".
Rev Gavin told BBC Radio 4's Sunday programme: "...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 a number of members of the congregation who have written open letters complaining of the profound upset they experienced as people who are part of the Eucharistic community who had come to worship Christ."
Last week, Premier reported that the Scottish Episcopal Church said it was "deeply distressed" at offence caused by the Qur'an being read at the service but it stopped short of apologising.
Church Primus, Most Rev David Chillingworth, said the "decisions which have led to the situation in St Mary's Cathedral are a matter for the provost and the cathedral community".
The provost at St Mary's, Very Rev Kelvin Holdsworth, said the Qur'an readings were a bid to strengthen ties between local Christians and Muslims.
He said: "Such readings have happened a number of times in the past in this and in other churches and have led to deepening friendships locally, to greater awareness of the things we hold in common and to dialogue about the ways in which we differ."
Speaking at the time, former Bishop of Rochester Rt Rev Michael Nazir-Ali, was quoted by the BBC as saying: "The authorities of the Scottish Episcopal Church should immediately repudiate this ill-advised invitation and exercise appropriate discipline for those involved."
Speaking on Premier's News Hour, Rev Dr Gavin said: "I think it's one of my roles to play a part in the public sphere, contesting the space for Jesus.
"There are times when I engage in a public controversy, and at the same time I have an association with the royal household, there's a danger the two roles become incompatible.
"As time has gone on that actually to keep the royal honour, I need to conduct a more discreet life, or else if I want to speak out on matters of public importance, then I need to do it in a way that decouples me from the royal associations.
"It was clear in my mind that needed to happen."
Listen to Premier's Alex Williams speaking to Rev Dr Gavin Ashenden on the News Hour: