Speaking in the House of Commons, Labour's Ben Bradshaw expressed his disappointment that a report by Bishop's was rejected by the Church's governing body General Synod.
The report called for the Church to take a "fresh tone and culture of welcome and support" towards gay people, but retain its opposition to same-sex marriage.
Speaking during church commissioners' questions, Mr Bradshaw said: "Was it not very significant that it was the clergy, who are in the frontline of providing pastoral care to their parishioners, who voted down the bishops' paper?
"And isn't it increasingly untenable for our established church, which enjoys significant privileges in this country because of its established status, to continue to discriminate against its own members simply because they happen to be gay?"
Dame Caroline Spelman, who represents the Church in the Commons, responded by saying: "This is a really serious matter and we should heed what the Archbishop of Canterbury, as the head of the Anglican Communion, said about the need to have radical Christian inclusivity.
"The Church of England is working towards a culture change which is inclusive within the current legal and doctrinal context."
Criticism also came from Labour MP and former trainee vicar Chris Bryant and Conservative MP Robert Jenrick.