The Bishop of Grantham, who on Friday became the first Church of England bishop to reveal he is gay and in a same-sex relationship, has said he "understand[s]" the backlash he has already received from some conservative Christians.

Bishop Nicholas Chamberlain told the Guardian on Sunday: "There has been direct response – I've had a lot of emails – which has been concerned, or anxious, and even angry, but not very much of that and I do understand that. I haven't had time to take it all in yet."

A statement from conservative group Gafcon, the Global Fellowship of Confessing Anglicans, has condemned Chamberlain's appointment.

"There are aspects of this appointment which are a serious cause for concern for biblically orthodox Anglicans around the world, and therefore we believe that this appointment is a major error," it said.

"I read it and listened to the news," Chamberlain said of this statement. "I can well understand what is being said by my brothers and sisters in Christ."

During a sermon at St Mary and St Nicolas church in Spalding on Sunday, Chamberlain spoke from the Gospel of Luke, and said there was "a cost to following" Jesus. "It will be different for everyone but it will be there," he said, according to the Guardian.

"I've been sitting with this gospel over the last few days: they have been interesting days. I hope you will forgive me that my words are not as polished as I would have chosen to be. They are what they are."

He also referred to a time that he had used the word "hate" in a sermon while training to be a vicar. A member of the congregation told him "that the word 'hate' was not appropriate on the lips of a Christian, and especially not on the lips of a Christian minister," Chamberlain recalled.

"I'm grateful to him for reminding me of my responsibility, for making me stop and reflect. So it is that Jesus' words today made me stop, think, reflect."

The bishop's coming out made headlines across the UK but he told BBC News he had never sought to make it a secret. "My focus and priority has been on my ministry, on serving God, on serving God's people. And I do that, as I always have done, as a gay man," he said.

He lives within the guidelines of the bishops of the Church of England which stipulates that gay clergy must be celibate, and Archbishop of Canterbury Justin Welby sad he was "fully aware of Bishop Nick's long-term committed relationship".

Chamberlain's appointment last November was "made on the basis of his skills and calling to serve the church in the diocese of Lincoln," Welby said. "He lives within the bishops' guidelines and his sexuality is completely irrelevant to his office."