Atletico Madrid coach
Falcao scored 36 goals in all competitions for Atletico last season after his club-record
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 UEFA 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 Saturday's (AEST) European Super Cup against UEFA Champions League winner 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,
"Chelsea are a powerful team both football-wise and economically, and we, with humility and hard work, will try to have a good game."
The trial of Franck Ribery and Karim Benzema for having sex with an under-age prostitute opened on Tuesday but was immediately suspended pending resolution of a point of law which may result in charges against the footballers being dropped.