The reigning La Liga champions failed to register a single shot on target as bottom side Levante won for only the second time in 24 games this season courtesy of Gonzalo Melero's second-half goal.
"We played poorly. We lost an excellent opportunity to put ourselves in a good position in the league and we will have to make double the effort to make up for today," said Simeone. "You have to be self-critical, see the reality. Some will think it's impossible to reach the Champions League, but I say no. It can be done, but you have to prove it with facts because words are boring."
Atletico are level on points with fourth-placed Barcelona but have played a game more than the Catalans.
It was a seventh league defeat of the season for Atletico, who host Manchester United next week in the first leg of their Champions League last-16 tie.