Carlo Ancelotti's side surrendered their position at the top of the table last weekend, going down 1-0 at Athletic Bilbao.
That defeat allowed fierce rivals Barcelona to usurp them at the summit as Lionel Messi's hat-trick inspired them to a 6-1 hammering of Rayo Vallecano.
Real then suffered a second successive defeat on Tuesday, as Schalke triumphed 4-3 in the Bernabeu in the second leg of the UEFA Champions League last 16 tie.
The defending European champions were able to edge through 5-4 on aggregate after their 2-0 success in Germany three weeks previously, but the home faithful were quick to show their discontent at the display.
"Sometimes you have to suffer and this will make us stronger," said Luka Modric, who made his first appearance since suffering a thigh injury in November.
"We have to get back to playing the way we were at the start of the season. We have a lot of quality and I think that we're going to see a much better Real Madrid in the next game."
That game sees Real host a Levante side just one place and one point above the drop zone, while Real's rivals Barca visit Eibar, whose run of seven straight league defeats has seen them slip towards danger.
Barca, however, are in fine form, with 15 wins from their last 16 outings across all competitions helping them to gain a slender one-point lead over Real.
The race for third place - and the final automatic Champions League qualification berth - remains wide open after last weekend's 1-1 draw between Atletico Madrid and Valencia.
Reigning champions Atletico look to have dropped out of the running for the title, but they are a point ahead of Valencia in the battle for third.
Valencia host Deportiva La Coruna on Friday and Atletico travel to Espanyol 24 hours later.
At the wrong end of the table, bottom club Cordoba head to Malaga in a bid to end their own seven-match losing streak, while fellow relegation candidates Granada and Almeria take on Rayo and Villarreal respectively.
Elsewhere, Celta Vigo welcome Athletic, Sevilla host Elche and Real Sociedad visit Getafe.
