Atletico are possibly still suffering with a hangover from their Spanish Super Cup final defeat to arch rivals Real Madrid, having resumed their La Liga campaign with a surprise 2-0 defeat at 16th-placed Eibar.
Last weekend's setback left them eight points off leaders Barcelona and Real with little chance of challenging for the title, and now they have been knocked out of the cup.
It may not have been the absolute strongest side Simeone could have put out but Atleti should still have taken care of the third-tier club, particularly having taken the lead through Angel Correa.
That advantage took more than an hour to materialise, however, and Julen Castaneda struck back late on for the hosts to send the game into extra-time.
Lucas Giffard made a number of saves to keep Cultural in it and Sergio Benito made Atletico pay for their failures in front of goal with the winner in the 108th-minute.
It was the earliest exit from the Copa del Rey suffered by Atletico since 2011-12, when they last lost to a third division club, Albacete, before Simeone had taken charge of the capital club.
The Argentinean tactician admitted that his side failed to take their opportunities but had no complaints with the result.
"Cultural deserved the win," Simeone said. "We couldn't score, and that is absolutely my responsibility."
Diego Costa is closing in on a return to action following a back injury although Atletico have been strongly linked with a move for Paris Saint-Germain's wantaway striker Edinson Cavani in this transfer window.
Whether that move goes ahead remains to be seen, although Simeone hinted he was at least happy with his current squad after the shock Cup exit.
"We have no other option other than to keep working," Simeone added. "I have a great squad and the results will come soon."