The German champions trounced the Spaniards 7-0 on aggregate to meet Borussia Dortmund in the final at Wembley.
Alves said that Bayern's clinical edge in front of goal was the difference across the two legs.
"Bayern were better than us throughout the tie," he told UEFA.com. "The only thing left for us is simply to salute them and congratulate them.
"Bayern have a great team. It's just another indication that this great tournament continuously makes you face the most powerful rivals.
"We played with a lot of intensity tonight but we didn't score and that's been the difference in this leg. They had their chances and they took them clinically."
In La Liga, Barca are 11 points ahead of Real Madrid with five games left to play.