Christian Concern says it is "deeply disappointing" the Church did not speak out as strongly on gay marriage as it has on payday lenders.
The advocacy group said the headlines around the Archbishop of Canterbury's criticism of payday lender Wonga this week demonstrated the potential impact of the Church if it had made similar statements against the legislation that brought in gay marriage this month.
Archbishop Justin Welby said in an interview in Total Politics this week that he wanted to "compete" Wonga "out of existence".
The story was widely publicised in the press but also caused some embarrassment for the Church of England when the Financial Times revealed the Church had indirect links to Wonga through its stake in a venture capital fund that has invested millions of dollars into the payday lender.
Head of Christian Concern, Andrea Minichiello Williams said: "We called on Archbishop Welby and the bishops many times, asking them to stand strong for marriage and speak out.
"The news this week shows the possible impact they could have had on the marriage debate. It's deeply disappointing that they didn't take the lead and make similarly robust statements about marriage when it mattered."
Christian Concern also strongly criticised the Prime Minister's plans to "export" gay marriage abroad.
David Cameron said in an address this week that he wanted the team of ministers and officials that put the gay marriage bill together to now work on promoting similar legislation in other countries.
Christian Concern said: "It's important that not just David Cameron, but also his advisers, know that there will be a political price to pay for such disregard of those who believe in traditional marriage."
The group is not the first to accuse the Church of England of not being strong enough in its defence of traditional marriage.
The chairman of the Global Fellowship of Confessing Anglicans and Primate of Kenya, Archbishop Eliud Wabukala said: "We are painfully aware that the Episcopal Church of the United States and the Anglican Church of Canada continue to promote a false gospel and yet both are still received as in good standing by the Archbishop of Canterbury.
"Furthermore, the Church of England itself, the historic mother church of the Communion, seems to be advancing along the same path.
"While defending marriage, both the Archbishops of York and Canterbury appeared at the same time to approve of same-sex Civil Partnerships during parliamentary debates on the UK's 'gay marriage' legislation, in contradiction to the historic biblical teaching on human sexuality reaffirmed by the 1998 Lambeth Conference."