The Argentine admitted he made errors during the early stages of the match and stressed that the defeat was not caused by Falcao's omission from the starting team
Two goals from Valdo and Arouna Kone in the opening 10 minutes gave Levante the victory and saw Atletico fail to move above their opponents in the race for a Champions League post net season.
"My players did not disappoint me at all, quite the contrary," Simeone told reporters after the game.
"I am responsible for what happened in the first 10 minutes because I could not make my players respond in a proper way.
"Right after that, the team improved and in the second half we gave a good account of ourselves, considering we were playing away from home."
Simeone then revealed that Radamel Falcao only came on as a second-half substitute because of a flu and played down the Colombian striker's absence from the starting lineup.
"He was not at 100 per cent and we understood that we would use him at the end if it was necessary and instead of him deploy Eduardo Salvio, who was fresher," Simeone explained.
"But the first 10 minutes would have been the same even if we had Falcao."
Atletico, who sit seventh in the Liga standings, will host Real Madrid on Wednesday.