Alba, who scored a late consolation for Barca last night, says his side's cup exit will provide them with added motivation for their European clash.
"We've given our all and it wasn't to be, this defeat will make us stronger for the Champions League," Alba said.
"These are two key games which we've lost but there's still the return leg against Milan to come which I'm sure will go better.
"If we score an early goal we will have a good chance of getting through, I have a lot of hope.
"The team have shown they can win any tie."