Liverpool were on the front foot again in the 15th minute following trickery by Adam Lallana, whose deft cross was volleyed goalwards by Woodburn, floating just wide of the far post.
Jurgen Klopp's side fell behind against the run of play thanks to some slack defending. Danny Ward produced a reaction stop to keep out Angel Correa's initial strike and tip it onto the bar, but when none of his teammates cleared the rebound, Bare pounced and nodded it over the line.
Liverpool made a flurry of substitutions in the second period and created more in front of goal, coming close straight from the restart when Henderson picked out Solanke with a long ball and the youngster hit it on the turn, his effort deflecting over for a corner.
Firmino stepped up and sent Moya the wrong way to level the match at 1-1, and that is the way it stayed after 90 minutes.
Atletico were clinical with their spot kicks, scoring all five, while Liverpool could only manage four.
Henderson was the guilty party, placing his kick too close to Moya and getting little power behind it.
It fell to Filipe Luis to seal the Audi Cup for Atleti, and he made no mistake from 12 yards, taking his time with his run-up before blazing the ball beyond Ward's reach.