Diego Simeone's side, chasing a first championship since 1996, could have ended their near-20-year wait with a home win over Malaga as Barcelona were surprisingly held to a goalless draw by Elche.
However, the destination of the trophy will be decided next Sunday after Bernd Schuster's men earned a 1-1 draw.
Toby Alderweireld's headed home a first league goal to earn a point but a host of missed chances, including Adrian Lopez's late strike being tipped over by Willy Caballero, left a feeling of two points dropped rather than one gained.
Another side who failed to capitalise on Atletico's profligacy were city rivals Real Madrid, who saw their championship hopes extinguished by a 2-0 loss at Celta Vigo.
Carlo Ancelotti's men only had themselves to blame as mistakes from Sergio Ramos and Marcelo gifted Charles a double.
While the draws earned by Elche and Malaga will be remembered for their impact at the top, they also guaranteed both sides' Liga status for another year.
Juanfran's last-gasp goal sent the former to a 4-3 defeat against relegated Real Betis, his strike coming after goals from Javi Guerra, Pena and Javi Guerra had offset a Pena own goal, plus efforts from Jorge Molina and Ruben Castro.
Osasuna, currently occupying the final relegation slot, were grateful for Javier Acuna cancelling out Diego Colotto's opener to earn a 1-1 with Espanyol, for whom a point was enough to secure top-flight football next year.
In the day's other game, Athletic Bilbao and Real Sociedad drew 1-1 as Imanol Agirretxe's 75th-minute equaliser ensured the spoils were shared after Iker Muniain had stuck for the hosts.
