Falcao, who won the competition with FC Porto a season ago, scored twice in front of the team's fans at the Vicente Calderon to give his side an advantage ahead of the return leg next week.
However, the Colombian has warned his teammates against becoming complacent.
"Great effort tonight!!!" he wrote on Twitter.
"We got at least 90 minutes ahead, we should be very careful to protenct our advantage! C'mon Atleti!"
Meanwhile, the Madrid outfit are in eighth place in La Liga.