"Nothing about what the primates have said will change the actions of General Convention that have, over the past four decades, moved us toward full inclusion and equal marriage," a statement said.
The Church has been suspended from full involvement in the Anglican Communion for three years following a meeting of the primates in Canterbury.
It came about after The Episcopal Church in the United States went against other churches in the Communion by authorising its clergy to perform same sex marriages in July last year.
Revd Gay Clark Jennings, president of the Episcopal Church's House of Deputies, said: "This news may be painful for some of us, particularly for LGBT people who have been excluded too often and for too long by families, churches, schools, and other institutions mired in homophobia.
"It may also be hurtful or unsettling to those of us who value our mission relationships with Anglicans across the Communion.
"I want to assure you that nothing about what the primates have said will change the actions of General Convention that have, over the past four decades, moved us toward full inclusion and equal marriage.
"And regardless of the primates' vote, we Episcopalians will continue working with Anglicans across the globe to feed the hungry, care for the sick, educate children, and heal the world.
"Nothing that happens at a primates' meeting will change our love for one another or our commitment to serving God together."
The primates decision means the Episcopal Church will not be allowed to serve on decision making committees or speak for the Communion on issues of doctrine.
But the Church has come out defiant against the punishment and said it will continue to serve fully on the Anglican Consultative Council, the worldwide body of bishops, clergy and lay people that facilitates the cooperative work of the churches of the Anglican Communion.
Revd Jennings said he was planning to attend the next meeting in Zambia and intended to "participate fully".
He added: "The people most likely to suffer from this news are faithful LGBTI Anglicans and their allies, especially in Africa.
"I count many of them as my friends and colleagues, and today I am especially praying that this new message of exclusion does not fuel more hatred and homophobia and make them even more vulnerable to violence and discrimination than they already are."
The Archbishop of Canterbury attempted to pre-empt accusations of homophobia by apologising to LGBTI Christians at a press conference following the meeting.
Most Revd Justin Welby said he finds it a "constant source of deep sadness that people are persecuted for their sexuality."