A 3-0 win over bitter rivals Real Madrid at the Santiago Bernabeu on Wednesday gave the Blaugrana a 4-1 aggregate triumph and the chance to lift the trophy for a fifth straight season.
Madrid might be in the midst of a similar streak when it comes to the Champions League but Spain left-back Alba feels they badly wanted to stop Barcelona's march on home soil.
"The excuse that it's an insignificant trophy doesn't cut it. We have suffered. In general, we've been good."
Long-serving midfielder Sergio Busquets agreed with that assessment after a Clasico where Barca's clinical edge – typified by Luis Suarez's brace – held sway.
"I'm happy for what it means, getting into another final," he told Sport.
"Playing at the Bernabeu is as difficult as it gets but the team's performances have been great and we can't ask for more in recent years.
"Madrid were better in possession, we struggled to stay together and control the counters. But they didn't score and when you miss this is what happens.
"It was one of the games here that we have suffered most in and one in which we've had the least possession of the ball."
Alba added: "We've won by three goals, that's not easy. Ultimately, we've won by a big margin. It's a very good result for us, it makes us stronger.
"We were the better side against a great rival, which is difficult in their stadium. They're always a complicated team and we have won in a convincing way."