The Rt Revd Michael Perham said they "underestimated how uncompromising and hurtful" the statement would have felt to some.
It made clear same-sex marriage would not be treated the same as the union of a man and a woman.
"No change to the Church of England's teaching on marriage is proposed or envisaged", it said.
Bishop Michael said: "My own view is that what is needed in the Church at present is gracious restraint.
"We need a cool and calm period in which to explore the issues.
"To those among clergy and ordinands contemplating entering a same-sex marriage I would say, Might you hold back while the Church reflects? Gracious restraint.
"To those who might make a complaint against a priest who, despite that, does enter such a marriage I would say, Might you hold back while the Church reflects? Gracious restraint.
"To those who contemplate leaving the Church of England because of its perceived position I would say, Might you hold back while the Church reflects? Gracious restraint."
He added the Church of England would now have to facilitate conversations at a national and diocesan level to reflect on the interpretation and application of Scripture.
He wants the Church to listen to the world of medicine and science on homosexuality.