Family and friends gathered at the Greenlane Christian Centre in Auckland this morning to farewell Ms Thomas, whose remains were found inside plastic containers in the Waitakere Ranges just under two weeks ago.
Her three sisters and mother were at the funeral, which was led by Pastor Terry Calkin.
He told mourners that violence never solved problems, "but always lurks beneath the thin layer of civility that we call society".
"That's why we have a police force, to ensure we all have a modicum of peace in our lives, and what a remarkable job the police have done under the leadership of Inspector Mark Benefield.
"Sir, you and your team have put a passionate and caring face on the otherwise sometimes brittle image of enforcement. We thank you and honour you today for the often thankless job you do in our community.'
Mr Calkin said Ms Thomas had suffered the ultimate act of another person's selfishness.
"Selfishness is innate in all of us - it infects and affects all of us.
"The Bible has another word for it. It is called sin. It's when you think that what you want is more important than what anyone else wants."
All of mankind suffered from the deep needs of security, self worth and significance, but the Christian message was that it was only out of a relationship with God that a person's needs could be met, Mr Calkin said.
"And so today we farewell another of God's children - one who, like us, was seeking to have her deep needs met. Another's selfishness brought that quest to an untimely end. We now commend the soul of our sister and daughter, Carmen Thomas, in the care of a loving and gracious God."
Ms Thomas leaves a five-year-old son, Jack.
She is also being farewelled in services in Whitby, England, and in Melbourne.
Her body is expected to be taken to her birth country, South Africa, where her mother Teresa Scott lives, for burial.
The man charged with Ms Thomas's murder, her former partner Brad Callaghan, remains in custody following a brief hearing in the Auckland District Court yesterday.
