Ousmane Dembele restored Barca's lead in the 64th and looked to have sent Ronald Koeman's side provisionally top of the standings but Levante came back at them and equalised again when striker Sergio Leon netted at the near post in the 83rd.
"This feels terrible, it's very difficult [to win the title] now," said Barca midfielder Sergio Busquets.
"We wanted to win and put pressure on the other teams but weren't able to and errors cost us dear, as has happened too many times this season. Teams keep scoring too easily against us."
Barca had clawed their way back into the title race with a sensational run of results since January but their resurgent challenge has unravelled in their last four games, in which they have taken five points.
Koeman's side gave away the lead in a shock 2-1 loss to visiting Granada on April 29 and after beating Valencia 3-2 in their next game were held 0-0 at home by Atletico on Saturday, missing a chance to go above Diego Simeone's side in the table.
Busquets, who wore a protective mask against Levante after sustaining a head injury versus Atletico, admitted Barca's opportunity to win the title had practically gone.
"We have very few chances of winning the league now and it's all our fault, we made lots of errors with our positioning and we lost concentration" he added.
"It wasn't just tonight, we've let a lot of points slip away from us this season, too many to fight to win the league."