A 2-2 draw in the second leg against Sevilla was enough to send Atletico through to the final 4-3 on aggregate where they will face rivals Real Madrid.
The Colombian was happy with the way his side unnerved Sevilla during the clash, which was most noticeable when Gary Medel reacted badly to being sent off.
"Being in the final is very important for Atletico, [so] we are pleased and we are proud," Falcao said. "The end of the match was ugly, but it doesn't matter.
"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."
Real Madrid progressed to the final after beating Barcelona in the other semi-final clash.