Dr Carey's assertion to the TUC Congress that employers had a "moral responsibility" to recognise unions was compared unfavourably with the Church of England's refusal to recognise the MSF union.
Roger Lyons, general secretary of the union, who claims 400 members in the Anglican communion, called on the Archbishop to "practise what he preaches". He accused Dr Carey of presiding over a medieval system for dealing with priests and argued that his support for union rights sat uneasily with the church's "hire and fire" approach to management.
"In commending to others what he will not allow his own employees, he will be seen as acting hypocritically. The priest's vocational commitment is often exploited. There is clearly a problem of poverty pay."
The Rev Stephen Trott, the MSF clergy section chair, said priests were the only category of workers in the country who enjoyed no employment rights. "The church must put its own house in order."
Mr Lyons' attack and the comments by Mr Trott contrasted with the standing ovation afforded Dr Carey by the 800 TUC delegates in Brighton, some of whom ventured that union leaders should seek to emulate the passion displayed by the Archbishop.
In his address Dr Carey, a former member of both the old Electrical Trades Union and Nalgo local government union, said that Christian social concern dictated that workers should be allowed an input into decisions which affected their lives. They should not be "denied a right to be represented by a trade union of their own choice in dealings with their employers".
He added: `I believe that, in broad terms, employers have a moral responsibility to recognise the chosen representatives of their employees."
This was widely interpreted as an endorsement of union recognition laws planned by the Government and opposed by many employers.
Told of Mr Lyons' criticisms, the Archbishop said: `I hope the consistency of my argument speaks for itself. I recognise the right of unions everywhere."
A spokesman for the church pointed out that successive industrial tribunals had decided that priests were not employed by the church but worked for God. "In a sense they are self employed, but have a stipend from the church so that they can lead a reasonable life while they are carrying out their ministry."Reuse content