The England international, who grew up supporting the Reds, opted instead to join Tottenham Hotspur and has since enjoyed a period of prolonged success.
Ayre claims that Alli had not shown enough in his short career at MK Dons to warrant the money he was after, and admits that there will always be an element of regret due to the success he has enjoyed in North London in the two years since.
"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," he told a lecture at Liverpool's St George's Hall.
"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."
Ayre also admitted that selling Luis Suarez to Barcelona in 2014 was his "hardest" piece of business during a decade at Anfield, which ended earlier this year.