On Friday the Church's bishops published a document that ruled out any change to the teaching on marriage but suggested a "fresh tone and culture of welcome and support" for gay people.
The report did not recommend how this could be done and instead called for further reports.
It will be presented to the Church's General Synod, which starts on February 13.
New teachings on marriage and relationships should also be drawn up to replace those introduced in the 1990s, it suggests, but this will not mean the Church accepting LGBT relationships.
It has taken three years of discussions for the bishops to publish this document, including the "shared conversations" - discussions which the church held in secrecy.
Beeching, who has become a prominent Christian LGBT campaigner since revealing her sexuality in 2014, said the report was "very disappointing".
Speaking with Premier she accepted that radical change was not expected but "it was a shock to see absolutely zero change offered".
"It's also confusing to read that they want a "fresh culture of welcome and support" for LGBT people, yet aren't reflecting that in church teachings. It requires serious mental and emotional gymnastics to hold that oxymoronic statement together."
She said many LGBT people will feel betrayed by the Church of England after they had agreed to share their experiences with more conservative members.
Beeching added: "For LGBT Christians this isn't a piece of paper, it's our lives - I can personally say that for me, documents like this affect my physical and mental wellbeing on a deep level.
"It's very painful to love Jesus, love the church, and yet feel rejected and like a second-class citizen because I'm gay."
