The game finished 1-1 after 90 minutes, with Roberto Firmino's spot-kick cancelling out Keidi Bare's first-half opener for the La Liga side.
Liverpool captain Jordan Henderson saw his penalty saved by Miguel Angel Moya in the resulting shootout.
And Filipe Luis stepped up to net the decisive spot-kick.
Jurgen Klopp's side reached the final of the four-team competition after beating hosts Bayern Munich 3-0 on Tuesday, while Atletico progressed with a 2-1 win over Napoli.
Liverpool, who won the Asia Cup last month, will now prepare to face Athletic Bilbao in Dublin in their final friendly match before their league campaign begins at Watford on 12 August.
Meanwhile, Atletico will now travel to England to face Premier League newcomers Brighton in a friendly at the Amex Stadium on 6 August.
Liverpool suffered their first defeat of the pre-season campaign after losing 5-4 on penalties in the Audi Cup final against Atletico Madrid in Munich.