The Blues dominated the first half but could not make the most of their superiority, and they paid the price after going into the break goalless.
A couple of mistakes, including giving away a penalty, allowed the hosts to get their noses in front, leaving City looking to Tuesday’s trip to Crewe to sew up the group.
Academy Manager Mark Allen said, “It was not one of our better performances, and we made costly mistakes that ultimately punished us.
“We should have made our possession count in the first half, but we regrouped well after they had gone ahead although in the end it was not enough.
“We’ll have to see how Liverpool and Blackburn have got on over the weekend, but the lads have to focus their minds quickly on the game on Tuesday, which could clinch it for us.”