Zinedine Zidane's side are provisionally 14 points off the pace following that defeat on December 23, although they have played one fewer game due to their participation in the Club World Cup last month.
Los Blancos beat Gremio in Abu Dhabi on December 16 to claim their fifth trophy of 2017, a club record, but they have serious work to do if they are to retain the Primera Division title they won last May.
Here, Goal takes a look at everything you need to know ahead of their trip to Celta Vigo on Sunday...
REAL MADRID INJURIES
Captain Sergio Ramos suffered a muscle strain in Thursday's training session and will be sidelined for two to three weeks.
Meanwhile, striker Karim Benzema also misses out on Sunday due to an injury sustained in the Clasico defeat to Barcelona last month.
REAL MADRID SUSPENSIONS
Right-back Dani Carvajal is suspended for the trip to Balaidos following his red card in the Clasico loss to Barcelona before Christmas.
REAL MADRID POTENTIAL STARTING LINE-UP
With Ramos out injured, Nacho and Raphael Varane should start in central defence for Real Madrid away to Celta.
At right-back, meanwhile, there will be another opportunity for youngster Achraf Hakimi as Carvajal misses out through suspension.
In attack, Gareth Bale is set to start alongside Cristiano Ronaldo in the absence of Benzema, with the Welsh winger on target from the penalty spot against Numancia in a 3-0 win in the Copa del Rey on Thursday.
CELTA VIGO TEAM NEWS
Left-back Jonny went off with a minor hamstring problem in the 1-1 draw against Barcelona on Thursday night, but the defender should be fit to face Real Madrid on Sunday.
Celta, with no other injury concerns or suspensions ahead of their first Liga fixture in 2018, are just six points clear of the drop zone after 17 games in the Primera Division, but also only three behind eighth-placed Getafe.
The Vigo oufit, 3-1 winners away to Deportivo La Coruna in the Galician derby just before Christmas, could hand a debut to new signing Robert Mazan, a Slovakian left-back brought in from MSK Zilina this week.
TV COVERAGE & KICK-OFF TIME
Celta Vigo versus Real Madrid kicks off at 20:45 local time at Balaidos on Sunday and will be broadcast live in the UK on Sky Sports Football from 19:40 GMT.
In the United States (US), Celta against Real is live on BeIN Sports and kicks off at 14:45 ET.
BEST OPTA MATCH FACTS
Celta have lost their last six league games against Real Madrid, conceding 23 goals in those matches (3.8 per game). However, they have only failed to score in one of the six.
Real Madrid have failed to win in their last three away league games (drawing two and losing one), after winning each of their previous 13. The last time they failed to win in four away games in a row in La Liga was in 2008 (three defeats and a draw).
Of all the sides currently in La Liga, Cristiano Ronaldo’s best goals per game ratio in the competition is against Celta (1.88).
Iago Aspas finished the 2017 calendar year as the highest-scoring Spaniard in La Liga (20). The former Liverpool striker has scored in four consecutive La Liga games for the first time in his career (five goals in total).
Marco Asensio has scored more goals from outside the box than any other player in La Liga this season (three).