The Bianconeri were knocked out of the quarter-finals by Ajax, 3-2 on aggregate, after a 2-1 home defeat.
Bernardeschi told Sky Italia: “These are important signals. I think the President built this year, in recent years and will do in future years a project that will win the Champions League.
“I believe the Champions League will arrive in Turin. If it's not this year, it'll be the next and if not the next, then the one after.