Madrid are fourth in the table after their 1-0 home defeat, 16 points behind leaders and bitter rivals Barcelona. The gap could increase to 19 points if the Catalans triumph against Real Sociedad on Sunday.
Zinedine Zidane's side have struggled this season and have won one game in their last five in all competitions, against third division Numancia in the King's Cup.
"We have to focus on qualifying for next season's Champions League," Kroos told BeIN Sports USA. "I think this should be our goal for the rest of the season.
"Sixteen points is very far behind and it's not the moment to think about anything that is not the next game and returning to winning points to bring us close to Real Madrid's objective, which is to finish in the top four."
The hosts created chances against Villarreal but were kept at bay by superb goalkeeping from Sergio Asenjo, before Pablo Fornals' perfectly-executed chip consigned Zidane's side to defeat.
Madrid have only managed to accumulate 32 points after 18 matches, which is their lowest points total at this stage of the season since the 2005-06 campaign when they had 30.
Fans made their displeasure at Madrid's recent performances known at the Santiago Bernabeu, jeering and whistling as their team trudged off the field.
"Those in the upper echelons of the Madrid hierarchy are now firmly on the fans' side, laying the blame at the dressing room door as this crisis period unfolds," wrote Spanish newspaper Marca, of the mounting pressure on coach Zidane.
The Frenchman has repeatedly stated he has signed a contract extension at Madrid until 2020, although the club has made no official announcement.
Zidane has also said the league title is out of Madrid's hands and should they fall to Paris St Germain in the Champions League last 16, his position will be at risk.
(Editing by Toby Davis)
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