The poem was included in the funeral's order of service
Attempts to track down the author of She Is Gone have come to nothing, The Times newspaper has said.
Experts suspect it was written by an unknown poet, and that its popularity has spread on the internet by word of mouth.
But it was used because it reflected the Queen's thoughts on how the country should celebrate her mother's life, Buckingham Palace told the paper.
Click here to read the full poem
The verse was sent into the palace on a memorial card by a member of the public, the paper said.
It had previously been used to mark the deaths of a 52-year-old Scottish alcoholic, a 15-year-old high school baseball player, and an Australian glam rock star killed in a helicopter crash, it reported.
It formed a preface to the order of service, and began: "You can shed tears that she is gone or you can smile because she has lived.
"You can close your eyes and pray that she'll come back or you can open your eyes and see all she's left."
Do you know who wrote She Is Gone? If so, e-mail entertainment.news@bbc.co.uk.
Alan Jenkins, a poet and deputy editor of The Times Literary Supplement, described it as "a nothing piece of writing".
But Poet Laureate Andrew Motion said its worth depended on the comfort it gave to the bereaved.
The Times said it searched the Poetry Library in London, which records every poem written in English since 1912, but found no record of it.
They also consulted The Poetry Society, Granger's Index to Poetry and Literature Online - all with no success in tracking down its origin.
"I understand that Her Majesty found the poem in a memorial service card," a Buckingham Palace spokesperson told The Times.
"It very much reflected her thoughts on how the nation should celebrate the life of the Queen Mother. To move on."
TV coverage
The Queen Mother's funeral, which was broadcast live on TV in the UK on Tuesday, was watched by 10 million people, according to unofficial overnight viewing figures.
The BBC, which came under fire for its coverage on the day of the Queen Mother's death, attracted an average of five million viewers for its coverage, peaking at 7.1m viewers.
ITV1's coverage was seen by an average of 2.5m viewers, peaking at 3.3m viewers.
A further 8.8 million watched review programmes on BBC One and ITV1 later in the day.
And a survey released on Wednesday found that 64% of the public thought that the BBC's coverage of the death was "about right".
Some 11% said it was disrespectful, while 8% thought it was too respectful, according to Mori.
She is Gone
You can shed tears that she is gone
You can close your eyes and pray that she'll come back
Your heart can be empty because you can't see her
You can turn your back on tomorrow and live yesterday
You can remember her and only that she's gone
You can cry and close your mind, be empty and turn your back
By Anonymous
or you can smile because she has lived.
or you can open your eyes and see all she's left.
or you can be full of the love you shared.
or you can be happy for tomorrow because of yesterday.
or you can cherish her memory and let it live on.
or you can do what she'd want: smile, open your eyes, love and go on.
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