Real Madrid are a point ahead of promoted Granada and Atletico Madrid after Diego Simeone's side failed to break down their well-drilled local rivals.
La Liga: Real Madrid are now four points clear of Barcelona after five games played.
Karim Benzema's brace helped Real Madrid secure three points at home against Levante.
Zinedine Zidane said he believes Gareth Bale will now stay, with the Spanish transfer window closing on September 2.
Real Madrid's response to Barcelona winning the title on Saturday night was to slip to a 0-1 defeat at Vallecas and fall 18 points behind La Liga's newly-crowned champions.
Real Madrid were mathematically ruled out of the title race after Barcelona beat Alaves on Tuesday while Atletico Madrid look likely to finish above them too for a second consecutive year.
Karim Benzema has been one of the few bright sparks in an otherwise dreary campaign for Real Madrid and his hat-trick at the Santiago Bernabeu took his tally to 30 goals for the season.
Real Madrid delivered another thoroughly underwhelming performance at Butarque to remain 13 points adrift of Barcelona.
Gareth Bale departed again to whistles with 14 minutes left, a conciliatory hand slap from Zinedine Zidane offering little consolation as he trudged off.
Real Madrid still lag 12 points behind leaders Barcelona, who are 10 clear of Atletico Madrid and heavy favourites to retain their La Liga title.
Santiago Solari was speaking at a press conference ahead of Tuesday's meeting with Ajax at the Bernabeu in the Champions League.
Karim Benzema and Vinicius Junior each scored in a 3-0 win over Alaves on Sunday.
Gareth Bale had been out since January 3 with a calf strain but made an instant impact off the bench for Real Madrid.
Karim Benzema, who has not played for France since being left out of the squad ahead of Euro 2016, has been dogged by controversy in previous years.
Leo D., who described himself as an agent of Karim Benzema, accused close friends of the Real Madrid forward of trying to grab him in Paris.
Real Madrid have taken maximum points from their opening 3 fixtures in contrast to the same point last season when they were already 5 behind Barcelona.
Karim Benzema netted twice and Gareth Bale scored a trademark goal as Real Madrid overcame an early scare at Girona to win 4-1.
Zinedine Zidane said Europe's premier competition always brings the best out of Real Madrid, who have won it 12 times.