The leaders' reverse in Valencia means Atletico's advantage over second-placed Barcelona, who drew 2-2 at home to Getafe on Saturday, was cut to three points with two games left, including the clash between the teams at Barca's Nou Camp stadium on the final day of the season.
Real Madrid are six points behind Atletico in third ahead of their match at home to Valencia later on Sunday and have another game in hand at Real Valladolid on Wednesday.
Because of the defeat at Levante, Atletico, who play at home to Malaga next weekend, will almost certainly have to beat Barca to win their first title since 1996.
"This is the best thing that could have happened to us because it will mean these next three weeks in our careers with Atletico are full of high intensity and emotion," Simeone, who side are also through to the Champions League final against Real on May 24, told a news conference.
"It is the ideal moment for men and footballers to stand up and show themselves," added the Argentine, who was in the Atletico team the last time they won La Liga.
"It was our turn to lose but, I repeat, there are three fantastic weeks left, with great emotion and football in its purest form.
"We still have our destiny in our own hands. We have to focus now on the first final against Malaga next Sunday."
Atletico and Real will both finish on 94 points if they win their remaining games, in which case Atletico would be champions as they have a superior head to head record.
Barca have a better head to head record against Real and drew 0-0 at Atletico's Calderon stadium in January.
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- Real Valladolid
- Real Madrid
- Nou Camp stadium