Victory for Atletico in Valencia would have meant they needed only a win at home to Malaga next weekend to secure top spot and render their final match at Barcelona the following week irrelevant.
However, an own goal from Filipe Luis in the seventh minute and a neat finish from David Barral 21 minutes from time meant Atletico failed to take advantage of Barca’s 2-2 draw at home to Getafe on Saturday.
With two games left, Atletico lead on 88 points, three ahead of second-placed Barca. Real Madrid, on 82 points in third, have two games in hand, a match at home to Valencia later on Sunday and a trip to Real Valladolid on Wednesday.
If in-form Real win their remaining four matches they will finish on 94 points and Atletico would have to beat Malaga and Barca to match their city rivals and would win the title thanks to a superior head-to-head record.
“We have to forget this and think about the next match,” Atletico midfielder Raul Garcia said in an interview with Spanish television. “We have to keep going, win the next game and, after that, go all out for the final one.”
Under coach Diego Simeone, Atletico are mounting their first genuine title challenge since they won a La Liga and King’s Cup double in 1996 with a team featuring the inspirational former Argentina captain.
In one of the best seasons in their history, they are also through to the Champions League final to play Real this month thanks to Wednesday’s superb 3-1 win at Chelsea’s Stamford Bridge stadium.
Simeone’s players did not seem to be feeling the effects of their exertions in London and started the Levante match with their usual intensity but fell behind when the ball ricocheted off Filipe’s chest at a corner and squirmed over the line.
A dominant Atletico had plenty of chances for an equaliser, including a Filipe shot cleared off the line by Levante defender Loukas Vyntra in the 63rd minute, before Barral controlled a cross from the left and fired past Thibaut Courtois.
Substitute Adrian curled a shot on to a post 13 minutes from time but Levante comfortably held out to climb above Rayo Vallecano to 10th on 45 points.
Tempers frayed at the end and there was a brief bout of pushing and shoving involving players from both sides but it quickly petered out and the disconsolate Atletico players trudged off as the Levante fans celebrated.