A Filipe Luis own goal and David Barral's 69th-minute strike condemned Atletico to their first loss since February, and breathed life into the Liga title race.
Atletico's fate remains in their hands, two wins from their final two games will be enough for a first title since 1996, though they face a daunting trip to barcelona on the final day.
Should Simeone's men slip up, it will likely give local rivals Real Madrid the chance to capitalise, though the Catalans remain in with a chance themselves.
Atletico will also face Real in in the UEFA Champions League final and Simeone hopes the pain of Sunday's defeat will inspire them to finish the campaign strongly.
"This defeat is the best thing to happen to us because it makes us live with high intensity and excitement in these three weeks," said the Argentinian.
"It's the ideal time for men, for players. We expect three fantastic weeks."
The Atletico boss was quick to praise a resolute Levante display at the Estadio Ciudad de Valencia, especially goalkeeper Keylor Navas, and insisted there were plenty of positives despite the loss.
"Levante scored a very quick goal and then defended well," he added. "It's true we had chances but their goalkeeper put in a great performance.
"We looked for different ways to level. We had the desire to create scoring chances.
"On this occasion we had to lose.
"We expect three finals and we have to focus on the first one, which is Malaga on Sunday.
"Ahead is three weeks of excitement, pure football. Now the league is much more fun."
