Alba argued, however, that the competition is only be looked down upon at the Santiago Bernabeu because of their lack of success in it of late.
Barca have won the trophy three times in the last five years to Madrid's one, with the current European champions disqualified last season for fielding an ineligible player.
"Sometimes a team loses a Copa tie and suddenly the competition is downplayed," Alba said after the win over Real Sociedad.
"It's not a good excuse to say that the Copa has no merit. As a Cule, I always want Real Madrid to lose."
Alba identified Madrid's conquerors Celta as his preferred opponent in the semi-finals before Barca were handed a crunch tie against Diego Simeone's Atletico Madrid.
"Luis Enrique was Celta coach, it's normal if you ask me about that," he said. "I would have liked Valencia."
Barca currently sit third in La Liga and return to top-flight action at lunchtime on Sunday when they take on Real Betis away from home.
Madrid, meanwhile, are top of the table with a game in hand, leading Sevilla by a point and the Catalans by two, and face Real Sociedad on Sunday evening.