The MLS club did well to frustrate Atletico coach Diego Simeone and his men but eventually lost the shootout 4-3 with 18-year-old striker Hector Hernandez converting the decisive spot-kick in the friendly match in California.
The reigning La Liga champions wasted a first-half penalty but were generally unable to break down the Earthquakes' defensive structure, in an impressive performance from Mark Watson's hosts.
Despite their impressive line-up, the Spanish visitors struggled to break open San Jose's defence in the first half, while the Earthquakes provided enough of a threat on the counter-attack to worry Atletico.
Garcia stepped up to take the spot-kick but his effort hit the post and Siqueira's rebound shot was parried wide by Bryan Meredith, despite San Jose's goalkeeper being stranded on the ground.
The Earthquakes held on for 0-0 at half-time and two minutes into the second period again sounded a warning for Simeone and his men with Tommy Thompson bursting clear through on goal, only to hit his one-on-one opportunity straight at Atleti's gloveman Miguel Angel Moya.
Atletico continued to have the majority of possession but the home side's stubborn defence was able to thwart the attacks of their more illustrious opponents.
An attack with 13 minutes to go was systematic of Atleti's problems with substitute Hernandez finding some space in the penalty area but San Jose's scrambling defence denied him a shooting chance and the forward's cutback failed to find a team-mate.
