Earlier this year, Dr Morgan authorised prayers which can be said with same-sex couples following a celebration.
He said he and his fellow bishops were accused of "ignoring Holy Scripture" by issuing the prayers.
In his final address as president of the Church's governing body before retiring, Dr Morgan said the Bible had more than one view on homosexuality.
Speaking at University of Trinity Saint David in Lampeter, Ceredigion, Dr Morgan responded to claims that he and his fellow bishops had been "swayed by the liberal culture of our age".
He compared biblical interpretations of same-sex relationships with those of slavery.
He said: "It absolutely will not do to quote texts from parts of the Bible in a simplistic way without reference to their contexts.
"In spite of all the passages in favour of slavery... you realise it is about freedom from all that diminishes and dehumanises people.
"No Christian I hope would today argue that slavery is good, but for 19 centuries the Church accepted it and defended it."
This meant that "one cannot argue that there is one accepted traditional way of interpreting Scripture", he said.
Last month, Dr Morgan announced that he would retire in January 2017.
The Archbishop of Wales has said the Church's view on same-sex marriage must change with popular opinion.