All this after taking an early lead at the City of Manchester Stadium.
Youth team coach Paul Clement told the clubs official website: "It was another high quality game and the two legs of this and the two legs of the semi-final have all had plenty of talent on show.
"Both teams tonight played attacking football, I thought us more than them. They played more by banking up and then playing on the counter-attack, which they did well, but we didn't create as many chances as we would have liked. We had a couple of decent claims for penalties but it wasn't our night.
"The cup run as a whole has been a great experience, getting to the final has been a fantastic achievement - we are just disappointed we didn't make it through the final hurdle. We will take a lot out of it and it will put the players in a good frame of mind for the future, and I hope for long professional careers.
"For several of the players there will be another bite at it next year, and for a couple of schoolboys another two bites. We will get the lads together tomorrow, reflect on the experience, what was good, what they learned from it, and move on."