Tottenham snapped up Alli from MK Dons ahead of Liverpool.
Ayre, speaking at a lecture in Liverpool on Wednesday evening, told his side of the story.
He said: “There was interest in the player, but where it got to was that the demands at that time were not fitting to what he had achieved at that point.
“We didn't feel the player matched that demand. It's easy to sit and say 'look what you could have bought', but how many players could you apply the reverse of that to? That's the truth."