The organisation, which says it is "standing together to retain and restore the Bible to the heart of the Anglican Communion", issued a statement following the Archbishop of Canterbury calling for repentance over missionary bishops at the Communion's Primates' Meeting on Friday.
GAFCON said it's "hopes for the meeting had been disappointed".
Leaders of GAFCON and the Global South met in Cairo last month to pray that "the outcome of the upcoming [Primates] meeting would be decisive and lead to coherent and responsible action regarding the issues which continue to tear apart the fabric of the Communion, issues that have eternal consequences".
Most Rev Justin Welby didn't specifically name people in particular who have become bishops without the permission of the bishop in the diocese or province, but rather from another bishop across the border.
However he condemned those who had.
Speaking to the heads of 33 Anglican provinces around the world, Archbishop Welby said: "The problem is where... one group subverts the efforts of another church group.
"Whether it's us doing it to others or others doing it to us is irrelevant.
"Either way that is harmful to our partnership in mission and that is something that we all need to repent and seek renewal.
"Jesus created the Church to be one so that the world might know that he came from God... and that's really crucial, and failure to do that is a cause for repentance."
GAFCON said while the Primates' Meeting has been portrayed as "good disagreement" over issues of sexuality, and that the theological convictions underlying the different positions can be set aside for the sake of institutional unity, this was false.
The group added in a statement: "... this does not reflect the reality. We are not "walking together."
Rev Canon Andy Lines was consecrated as missionary bishop by GAFCON, to cater for disaffected Anglicans in Scotland, England and across Europe.
During the week long meeting that came to an end on Friday, the Primates also discussed issues such as climate change, human trafficking, the refugee crisis, persecution against Christians and violent conflict.
