Fernando Morientes was the last player to score five in a match playing for Real Madrid against Las Palmas in February 2002 and Falcao was the first to do so for Atletico as they thrashed Depor 6-0 to stay in second place, six points behind leaders Barcelona.
"I scored five in a game when I was little in Bogota," the Colombian known as "the tiger" said on Atletico's website (www.clubatleticodemadrid.com).
"And I got four playing for Porto against Villarreal but never five as a professional," he added.
"I was very excited when I came to Atletico Madrid. It was a personal challenge to play in this great league with such a lot of good players
"I am enjoying it. I have a great squad around me who are supporting me and helping me a great deal to develop as a professional."
Falcao took his tally in La Liga this season to 16 in 15 matches, three more than Real Madrid's Cristiano Ronaldo and seven behind top scorer Lionel Messi of Barcelona.
However, his exploits are certain to raise expectations that one of Europe's richest clubs will attempt to lure him away.
The 26-year-old has been linked with big spenders like Paris St Germain, Chelsea and Manchester City and even with Atletico's arch rivals and city neighbours Real.
Atletico coach Diego Simeone said the club were savouring Falcao's presence in the side.
"His people love him, his team mates respect him a great deal and they follow his lead on the pitch," Argentine Simeone, a former Atletico player who has revived the club's fortunes since taking over in December 2011, told a news conference.
"Today is an historic day for him," he added.
"I don't know if any other Atletico player will score five goals in a match. I hope that's the case.
"Falcao represents ambition, excitement, always wanting more. When the game allows and he has his chances he really is very difficult to mark." (Reporting by Iain Rogers, editing by Ken Ferris)