The Rev Margaret McPhee made the comment at a carol service at St Mary's Church, Stalham in Norfolk for Stalham Academy pupils on Monday night.
A parent on Facebook said she had "spoiled the magic" of Christmas.
The school said Mrs McPhee had promised "she will not be making any such comments in the future".
During the carol service, the curate asked children what they thought was the meaning of Christmas.
When a child answered "Father Christmas", she told them he was not real.
One parent said on Facebook that Mrs McPhee had "put me off taking my children to church just in case something else gets said".
But another showed support and posted: "I bet this Rev is feeling terrible. No-one spoils the magic of Christmas on purpose for children."
In a statement, Stalham Academy said it had received an "official apology" from Mrs McPhee..
The Ven Jan McFarlane, archdeacon of Norwich, said: "Margaret is a sensitive and sensible priest who let slip a comment which she immediately regretted.
"She apologised swiftly and wholeheartedly and regrets any distress her comments may have caused."

The flag was raised beside Stormont House on Friday morning to mark Belfast's Pride festival on Saturday.
Northern Ireland Secretary James Brokenshire approved the flying of the flag.
The move comes amid the continued deadlock over Northern Ireland's ban on same-sex marriage.
It also coincides with the first official visit of Taoiseach (Irish prime minister) Leo Varadkar to Northern Ireland.
Mr Varadkar is the Republic of Ireland's first openly gay taoiseach and will attend a pride festival breakfast event on Saturday morning.
Thousands of people are expected to take part in the main Belfast Pride parade on Saturday afternoon.
Northern Ireland is the only part of the UK where same-sex marriage is still banned.
The issue is one of the major stumbling blocks in the ongoing Stormont crisis, with Sinn Féin demanding that the DUP stop blocking a law change.
Before the Northern Ireland Executive collapsed in January, the DUP had used a Stormont veto known as a petition of concern to block motions to change the law on same-sex marriage.
The party has rejected accusations that it is homophobic and said that it is protecting the "traditional" definition of marriage between a man and a woman.
Stormont House is Mr Brokenshire's base within the grounds of the wider Stormont estate.
He said that while same-sex marriage was a matter for devolved government at Stormont, he hoped that the law would change.
"I voted for equal marriage in England and Wales and, like the prime minister, hope this can be extended to Northern Ireland in the future," he said.

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A trainee vicar who told primary school children Father Christmas does not exist has apologised for her "insensitive, off-the-cuff remark".
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A rainbow gay pride flag has flown at a Stormont government building for the first time.
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It's been a busy week in the world of entertainment - with the Love Actually cast reuniting, New York Fashion Week drawing to a close and awards ceremonies aplenty.