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Midfielder Xian Emmers scored the only goal just after half-time for the Nerazzurri, as Alberto De Rossi's side went out at the Mapei Stadium despite a spirited second half response.
"I told the lads to pick their heads up - they're all gutted," De Rossi said afterwards. "I've told them the truth. They've had a great season and lots of them will definitely play professional football.
"They have to pick themselves up because they've had an incredible campaign."
The Giallorossi have enjoyed a spirited rivalry with Inter all season - beating them in the final of the Supercoppa at the Stadio Olimpico, and then edging past them in the semi-finals of the Coppa Italia on the way to their victory in that competition - but were edged out this time around.
"It's still a very positive season," the coach continued. "Our players are highly sought after and that means a lot in an academy. They've all managed to show what they can do by having a positive season.
"It's a shame we couldn't put the icing on the cake by making the final. We would have liked to have retained our title. We're disappointed now but it's time to go again.
"Our opponents began very well and they caused problems for the lads with their physicality and forward passes. The game then evened itself out and we tried to knit our play together but we really got our final ball wrong in the first half especially.
"We have lots of ability but we lacked the finishing touch on the chances we created."
See some more photos from the game in the gallery below.
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