The Sheffield United midfielder was named in England's squad for the Toulon Tournament minutes after withdrawing from the Wales party.
But Page is still hopeful the dual qualified 19-year-old will become involved in the Welsh set up.
"He committed to play for England, but it doesn't mean the door is closed for Wales," said Page.
Page, who oversees all Wales younger age groups, explained Brooks, who has made four appearances for the Blades this season, had already committed himself to England when Wales announced him in their squad.
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"Unfortunately on this one we just missed out, but that is not to say in the future he will not be part of the Welsh set up," said Page.
"No doubt our paths will cross out there and I want him to go and have a good camp, but inevitably I want him to come and be part of the Welsh set up.
"I am disappointed we haven't got him this time, but we are not going to close the door on him and, like any of the young lads, they don't have to commit themselves to one country at this moment in time.
"Go and enjoy being part of both and then when you are ready, make your decision. That is what I will say to all the youngsters."
Page said he had sympathy for Brooks' predicament, but did not blame him for opting for England as he did not know he would be picked for Wales.
The former Wales captain is keen to recreate the environment of the senior squad to attract the best young talent.
"When he does come he will thoroughly enjoy it," Page added.
"You have to be committed to play for your country and that is what I expect from my players. If you do not show that commitment then I will question you. But until you make that decision, the door is always open."
The Wales under-20 squad will assemble for the Toulon Tournament on Wednesday.
Under-21 manager Robert Page insists the door is not closed on David Brooks playing for Wales.