The Tynecastle outfit's Under-20s, including five first-team regulars, lost out 8-7 in a penalty shoot-out to Rangers on Tuesday night.
Neilson, who has been promoted from his position of Under-20s manager to first-team head coach under a new structure that includes former Scotland manager Craig Levein as director of football, said: "It's hard to take for them but I said: 'you have two choices when you lose a game like that, you can either go away and feel sorry for yourself and spend your summer thinking what could have been, or you can use it as a motivation to go and get ready for next year and make sure you work hard. And next time you get into that situation, win the game'.
"I think the majority of the boys will choose the second option."
Speaking to Hearts TV, Neilson added: "They will grow from the experience of losing a penalty shoot out. Nobody will go through their career not doing it."