Children at Lumley Junior School near Chester-le-Street, County Durham, did not believe the Considerations For Increasing Participation In Women And Girls Football paper was real when they read it during lessons about gender equality.
Among the advice were tips such as offering stamps and prizes for players to keep attending sessions, allowing girls to wear casual clothing and using colourful bibs - but "make sure they are clean and smell nice".
The document also suggested some beginners might be put off by being hit by a heavy ball, so coaches should consider using smaller ones.
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Girls should be allowed to play music during football sessions, the paper suggested, and their games should be indoors in the winter.
One tip which particularly angered the Lumley pupils was "Allow girls the time to check their phones within a session or incorporate a Twitter break so participants can tweet about the session".
The Year 5 and 6 pupils were encouraged to respond to the FA as part of a writing project and Nancy, aged 10, gave the governing body both barrels.
She wrote: "I am absolutely astonished that you have the nerve to write all of that absolute rubbish about women and girls playing football.
"I am a girl myself, I like playing football and your Considerations For Increasing Participation In Women And Girls Football is totally wrong!"
She added: "We will not go to your training sessions just because you give us stamps!"
Her letter told the FA chief Martin Glenn in no uncertain terms that girls do not need to constantly update social media.
"Your tone of voice sounds as though you think we are brainless baby Barbies!"
Fellow Year 6 pupil Grace wrote: "We are not fussy about the smell of our bibs - would you be?
"And we are not afraid to get hit by a ball, so why would we need light ones; in case we break a nail?"
Amy, who loves the game and plays for the school and a team in Washington, said: "I didn't think it was real.
"I thought none of this would be said for boys' football. Some of the content was unbelievable."
Deputy head Carol Hughes said the pupils - girls and boys - were struck by the implied sexism of the document. "We kept thinking, what would they write for boys?" she said.
The school runs a girls' football team, and children of both sexes play keenly-contested games during lunchtime.
Mrs Hughes sent off the pupils' letters at the end of November, but has not yet had a reply from the FA.
She said: "I am incredibly proud of them, I just hope they get a response soon."
An FA spokesman said: "The FA is committed to doubling female football participation by 2020 and to growing the women's game at all levels, from elite to grassroots.
"The document is aimed at engaging young women who don't currently play football.
"It was created following research into women and girls playing football, with feedback from both participants and non-participants, and encourages a creative approach to increasing participation numbers.
"We're very pleased to see how many girls at the school play football and the passion for the game that they clearly have."