The prolific Colombian was thrilled and relieved after his goal helped Los Colchoneros edge a bad-tempered clash with Los Rojiblancos to book their place in the final
Falcao's 29th minute strike was crucial as it sent the away side into a 4-1 aggregate lead, which proved unassailable despite the hosts' comeback.
"Being in the final is very important for Atletico, [so] we are pleased and we are proud," Falcao told reporters after the match.
"The end of the match was ugly, but it doesn't matter," he added, referring to Gary Medel's incensed reaction to being red-carded as the match drifted away from the Andalusians.
Former Porto striker Falcao also admitted that Atletico's first-leg advantage and their opponents' increasing attempts to chase the game played into their hands.
"We had a good strategy. We knew they would try to win and that would give us chances, and we took advantage.
"I'm happy because we put in a lot of work and effort."