Sergio Ramos' free-kick had given Madrid the lead 10 minutes before half-time, but Humberto Osorio's late header rounded off a horrible evening for the visitors as Cristiano Ronaldo also hobbled off with an injury yesterday.
The draw leaves Real four points behind leaders Atletico Madrid and a point adrift of Barcelona with two games to play.
Real will be mathematically out of the title race should Atletico win at home to Malaga on Sunday and Atletico could be crowned champions for the first time in 18 years should Barcelona also drop points away to Elche.
"We failed to kill the game off, but it wasn't for the want of trying. The league is practically lost, but whilst mathematically it is still possible Real Madrid is obliged to fight."
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Real boss Carlo Ancelotti said he didn't believe Ronaldo's injury was too serious, but he also has injury worries over Pepe and Angel di Maria as they both ended the game with problems.
"We will have to see in the next few days with all of them," said the Italian.
Sections of the Spanish press were quick to criticise Ancelotti for making two defensive substitutions in introducing Asier Illarramendi and Marcelo for Isco and Karim Benzema respectively in the final quarter.
And he admitted his side sat too deep as they attempted to protect their lead in the final stages.
"We lost control, but I don't think it was a lack of attitude on the players' part.
"Iker (Casillas) didn't have a save to make in the whole game. I think the team played well, but at the end it became more difficult. We sat back too much and defended too deep and in the end conceded a goal from a set-piece.