Atletico, routed 4-0 by Paris Saint-Germain in their opening game of the tournament, went into the final round of Group B fixtures knowing they would likely need a big win to advance.
With PSG defeating the Seattle Sounders 2-0 elsewhere in Group B, that task proved beyond Diego Simeone's men in another sweltering midday kick off in front of 22,992 fans at the Pasadena Rose Bowl.
Former France international Antoine Griezmann scored the game's only goal, lashing home a Julian Alvarez cross in the 87th minute to give Atletico a victory that ultimately was in vain.
Botafogo -- who upset European champions PSG 1-0 in their second group game -- finished the group stage in second on six points behind the French giants, who top the section on goal difference.
Atletico, who also finished with six points, missed out on goal difference behind Botafogo.