The Colombian scored in a 2-2 draw at the Estadio Ramon Sanchez Pizjuan - a result that earned Atletico a 4-3 aggregate victory.
"Being in the final is very important for Atletico," Falcao told reporters. "We are pleased and we are proud.
"I'm happy because we put in a lot of work and effort."
Atletico will face city rivals Real Madrid in the final on May 18.