Messi, Barcelona held by Levante
But Atletico conceded a second-half penalty at home against Sevilla to also finish 1-1 and squander its chance to rise to the sole lead in the standings for the first time since September 2010.
Levante went ahead through Loukas Vyntra's 10th-minute header, and its staunch defense did enough to take a measure of vengeance for the 7-0 thrashing Barcelona dealt the team in the season opener.
Gerard Pique leveled for Barcelona in the 19th, but Levante defender Juanfran Garcia saved the visitors' two best chances in the second half.
''We were unlucky because we created scoring chances,'' Messi said. ''We did everything possible to win.''
Far from the side that Barcelona humiliated in August, Levante lived up to its reputation as one of the league's best defenses by packing its area and largely limiting the visitors to long strikes that either crashed into bodies or sailed harmlessly wide.
Joaquin Caparros' side claimed the early lead when Vyntra rose up over Pique to head Andreas Ivanschitz's corner kick down and beyond the diving goalkeeper Victor Valdes.
Pique made up for his slack marking by scoring an almost exact replica of the opener, jumping higher than a pair of defenders to redirect Xavi Hernandez's corner inside the far post.
Messi, in his fourth game back after a long injury layoff, worked a one-two passing combination in close quarters with Cesc Fabregas to manufacture Barcelona's best chance in the 59th, but goalkeeper Keylor Navas saved Messi's shot. Garcia was well positioned to block Xavi's follow-up attempt, and three minutes later the center back used his foot to turn away Messi's goal-bound strike.
Barcelona's frustrating night was summed up when Fabregas violently struck the dugout cover after coach Gerardo Martino replaced him with Sergio Roberto in the 73rd.
With Neymar and Andres Iniesta both unavailable due to injury, Martino turned to Cristian Tello and B-team forward Jean Dongou as late substitutes, but Levante held firm.