Falcao, who joined Atletico from Porto for €40million in the summer transfer window, opened the scoring after just three minutes of their Group I clash with Scottish outfit Celtic.
Falcao met a Diego corner to head past Hoops keeper Fraser Forster before Atletico added an insurance goal in the second half.
"I am happy to have scored," Falcao told Canal+.
"It is my first goal at the Vicente Calderon.
"It boosted our confidence as we got the lead early in the match and we managed to keep it.
"The important thing is that Atletico win and that we reach our goals game after game. If I score, that is even better."
Falcao failed to find the back of the net in Atletico's 1-0 defeat at Valencia last weekend. He is seen as a replacement for Argentina striker Sergio Aguero, who left to join Manchester City in the transfer window.