Midfielder Dani Ceballos added: "It looks like us changing our coach worked. We have recovered some sensations we had lost and we have got the three points. Now our objective is to win all the games left and finish the season as well as possible."
Real are third in the league standings with 54 points after 28 games, two behind second-placed Atletico Madrid who visit Athletic Bilbao later on Saturday and nine points behind leaders Barcelona who play at Real Betis on Sunday.
News of all that's transpired on and off the football field
The Catalans have kept five clean sheets in their last six games, which bodes well for their title run in.
La Liga leaders Barcelona beat Real Madrid 1-0 to all but knock their rivals out of the title race on Saturday, while second-placed Atletico Madrid stayed seven points behind the Catalans with a 2-0 win at Real Sociedad on Sunday.
News of all that's transpired on and off the football field
Chelsea coach Maurizio Sarri said the refusal of his goalkeeper Kepa Arrizabalaga to be substituted in Sunday's League Cup final was the result of a "big misunderstanding", adding that the Spaniard "was right but in the wrong way".
Barca feel familiar February blues as tiredness sets in
Barcelona have been haunted by their recent failures in the Champions League and there are concerning signs for the Catalans as they prepare for Tuesday's last-16 first leg away to Olympique Lyonnais.
Lionel Messi scored one penalty and missed another as Barcelona beat Real Valladolid 1-0 on Saturday to open up a seven-point lead at the top of La Liga.
Here are five talking points from the weekend in La Liga:
La Liga leaders Barcelona handed Real Madrid more hope in the title race as they drew 0-0 at Athletic Bilbao on Sunday, only avoiding defeat thanks to some outstanding saves by Marc-Andre ter Stegen.
Barcelona beat Girona 2-0 in a Catalan derby on Sunday to maintain their five-point lead at the top of La Liga, while Real Madrid thrashed Espanyol 4-2.
Here are five talking points from the weekend's action in La Liga.
IMAGES from La Liga matches played on Sunday
Struggling Rayo win at Valladolid after late penalty save
Midfielder Santi Cazorla gave the home side the lead in the fourth minute of the game, which was rescheduled due to Real's participation in last month's Club World Cup, by bending a wonderful shot into the bottom corner.
Real Madrid lifted the FIFA Club World Cup for a record fourth time on Saturday after thrashing local side Al Ain 4-1 in the final in Abu Dhabi with the help of impressive distance strikes in either half from midfielders Luka Modric and Marcos Llorente.
News of all that's transpired on and off the football field
Holders Portugal must face Ukraine and Serbia in a tricky five-team Group B while world champions France drew Iceland and Turkey in Group H. The top two teams from each group qualify automatically. Unlike previous tournaments, the playoffs to decide the four other spots will be contested between the most successful teams from the four divisions of the Nations League who have not already qualified.
Spain coach Luis Enrique promised evolution rather than revolution when he took charge of the national side following their disastrous World Cup campaign this year when they were eliminated in the round of 16.
News of all that's transpired on and off the football field
Chelsea's Marcos Alonso and Real Madrid's Nacho were notable absentees in defence, along with Atletico Madrid midfielder Koke.
News of all that's transpired on and off the football field
Real coach Julen Lopetegui has come in for fierce criticism this season, having presided over a run of five games without a win -- the team going eight hours and one minute without scoring -- before Tuesday's unconvincing 2-1 triumph over Viktoria Plzen that saw the team whistled off the pitch by their own fans.
Here are five talking points from the weekend's action:
Costa, Alba excluded from Spain squad
Leaders Barcelona and Real Madrid were held to draws while Sevilla made up ground on the top two and Alaves slipped after a promising start. Here are five talking points from the weekend's La Liga action.
Real Madrid, Barcelona and Atletico Madrid, find themselves in the bizarre situation of having made poor starts to the campaign
'We have to improve and become stronger in defence, which is the most important thing.'
La Liga champions Barcelona's domestic struggles continued as they dropped points for the third game in a row, drawing 1-1 at home to Athletic Bilbao on Saturday after Lionel Messi and Sergio Busquets had begun the match on the substitutes' bench.
Barcelona have been frighteningly good at home this season, scoring 15 goals in three games at the Nou Camp.
The Portuguese can expect a hostile reception in Valencia, who had to suffer 15 of his goals for Real Madrid and are returning to the Champions League for the first time in three years.
Iker Muniain gave Athletic a deserved lead in the 32nd minute by bundling the ball home after Real failed to get back in time to defend a counterattack.
Barcelona rode their luck to come from behind and win 2-1 at Real Sociedad on Saturday, continuing to banish their awful record in San Sebastian and maintaining their perfect start to the La Liga season.
Real play Athletic Bilbao while Barcelona visit Real Sociedad in fixtures that have often proved to be among their hardest away trips over the last decade.
Real Madrid have started the season flying with three wins from three games.
Fellow Spaniards at Chelsea convinced me to join club, says Kepa
Real Madrid goalkeeper Keylor Navas says the signing of Belgium keeper Thibaut Courtois has not affected his desire to remain at the triple European champions as he emphatically ruled out leaving the club in order to be assured of first team football.
Chelsea have signed Spanish goalkeeper Kepa Arrizabalaga for a world record 80 million-euro ($92.8 million) fee from Athletic Bilbao, the Premier League club said on Wednesday.