The champions have won only one of their first four matches and lie eight points behind Barcelona ahead of Sunday's visit to local rivals Rayo Vallecano - a deficit which will increase to 11 points if Barcelona win their home match against Granada tonight.
However, Real will be heartened by their 3-2 Champions League defeat of Manchester City at the Bernabeu on Tuesday, in which they came from behind to win in the closing stages.
Defender Pepe said after the success: "Things are going to change from now on. Now everyone is going to see a different Real Madrid."
Coach Mourinho raised eyebrows on Tuesday by leaving defender Sergio Ramos on the bench and picking teenager Raphael Varane.
And the Portuguese has another dilemma in midfield - he must also decide whether to start with playmakers Luka Modric and Mesut Ozil, who came off the bench and helped spark the comeback from 2-1 down, or stick with Sami Khedira and Michael Essien.
Opponents Rayo are in the unfamiliar position of being six places and three points above their more illustrious rivals - and right-back Tito believes all at the club should enjoy Sunday's contest.
He said: "We are expecting the best version of Real Madrid, the one that played so well on Tuesday - it doesn't matter who plays.
"It's true they haven't got into their stride in the league but they will soon find their rhythm."
Tito highlighted the never say die attitude of Francisco Jemez's team, which was in evidence on Sunday in the Primera Division game against Real's city rivals Atletico.
The Super Cup winners appeared to have the points in the bag when they led 4-0 at the Vicente Calderon - however, three Rayo goals in the final 10 minutes meant for an uncomfortable finish for the home support.
Tito explained on his club's official website, www.rayovallecano.es: "The other day against Atletico, with four goals against, we knew how to react. We never know when we are beaten.
"I hope there is a great atmosphere against Real. Let people come and support us."