Please Wait . . .
Ricard Sanchez was sent off as Atleti slumped to a shock reverse swiftly described by the Spanish media as a "disaster" among the very worst of Simeone's 502 games in charge of the club.
The long-time coach named a strong side, including record signing Joao Felix, but saw his team remarkably unable to register a single shot on target.
Copa failings are a familiar story by now, though, with the Rojiblancos losing to Cultural Leonesa last season. Meanwhile, they have not beaten a fellow LaLiga outfit in the competition since seeing off Elche in January 2017.
Simeone recognised Atleti are struggling in one-off knockout matches - also losing in last season's Champions League to RB Leipzig - but added the surprising qualifier that it would be an issue to consider only if he was still at the helm next year.
"Cornella played better," he said. "In the whole game, what they wanted was always done better than what we wanted.
"They took advantage of the set-piece situations and immediately found the goal.
"The boys tried to compete in the best way. In the first half, we had more chances, and in the second, it was rockier. It got difficult after the red card.
"This competition has not given us satisfaction in recent years but solutions will have to be found if we are here next year."
Saul Niguez, captain on the night, identified the same problem as he added: "We apologise to the fans. We never throw away competitions, but in these single-game editions we are not doing well."
Given Atleti's struggles, the decision to replace Joao Felix with 18-year-old debutant Mario Soriano 15 minutes from time prompted some discussion.
But the Portugal international mustered only one shot, which was blocked, prior to his withdrawal and failed to create a single chance - unlike his replacement.
Joao Felix epitomised the visitors' display as he completed just 13 of his 21 attempted passes and lost possession 13 times, winning none of his three aerial duels.
The change still appeared a big call, yet Simeone explained his star forward was struggling with an ankle injury.
"He was hurt," Simeone said. "We looked for a fresher guy. He had a bruised ankle and we wanted to find a guy in good condition."