Thierry Henry's men fell at the Wanda Metropolitano, as first-half goals from Koke and Antoine Griezmann sent Atletico through to the last 16.
The defeat meant Monaco have now gone 13 games without a win in the Champions League (10 losses, 3 draws), the longest ever winless streak for a French side in the competition.
13 - Monaco have won none of their last 13 games in the Champions League (D3, L10), the longest streak without winning ever for a French side in the competition. Curse. #ATLASM pic.twitter.com/Ikp5hluD3B— OptaJean (@OptaJean) November 28, 2018
Koke's goal came after just 87 seconds, and was the fastest Monaco have ever conceded in the Champions League.
The principality side did have a chance to cut the deficit to one goal in the second half, but striker Falcao missed a penalty to continue a dismal run from the spot.
The Colombian has now failed to score any of his three penalties taken in the Champions League, two of which were saved and one that was missed.
Monaco's last win the competition came in the 2016-17 quarter-final second leg against Borussia Dortmund, a 3-1 victory that sealed a 6-3 aggregate triumph.
Since that victory, though, Monaco have failed to win in Europe's top club competition, and now sit bottom of Group A with just one point through five of six games.
Monaco will look to end their streak on December 11, when they take on Dortmund in their final group stage match.