Falcao scored 36 goals in all competitions for Atletico last season following his club-record 40million euros move from Porto and the 26-year-old picked up where he left off with a starring performance in the Rojiblancos' second league game of the new campaign.
Falcao opened his account in the 19th minute with a brilliant individual effort, then doubled his tally in the 42nd minute with a far-post finish before completing his third hat-trick for the club with a 59th-minute penalty.
Simeone said: "Falcao had an extraordinary game, almost perfect."
Tiago netted the final goal of the game in the 84th minute as Atletico heaped more misery on Athletic having also beaten the Basque side 3-0 in May's Europa League final.
Falcao, who has now scored seven times in three matches against Athletic - including two in the Europa League final, said on his club's website: "It was a great night in which I scored three goals. I could have had more but I'm happy with the three.
"The whole team did well. We are very happy with this victory. Athletic are a very difficult opponent and we've been able to overcome them."
Next up for Atletico is Friday's European Super Cup against Champions League winners Chelsea.
Simeone dismissed any suggestion his side might have had one eye on that game heading into the league meeting with Athletic, saying: "We try to think game by game. And the best way to prepare for another big clash is to do well in the previous game.
"I especially liked all the guys who came off the bench (Adrian, Diego Costa and Tiago). We have to know that we have strength in the team because there are options, something that gives us optimism and from that we'll go into a match against the greatest team from England.
"Chelsea are a powerful team both football-wise and economically, and we, with humility and hard work, will try to have a good game."