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Atletico, who have failed to win at Villarreal since April 2015, are sixth in the table on 26 points from 16 games, five behind Liga leaders Barcelona who have two games in hand.
Atleti's 126 million euro ($138.88 million) signing Joao Felix failed to convert any of his six chances, including a glaring miss in the first half where he was unmarked in the box but somehow sent the ball over the bar from close range.
Atletico drew a blank in a 1-0 defeat at home to Barcelona in La Liga and in losing by the same scoreline at Juventus in the Champions League in their previous two games and coach Diego Simeone said the poor results were affecting his players.
"It's normal (that) when you are not getting results and are creating lots of chances but not finishing them off you start to feel anxious," he told reporters.
"The only way to calm ourselves down is through hard work, as at the moment we're feeling anxious and are lacking precision. Once we manage to calm ourselves down, we will be ourselves again."
The fixture had been pencilled in as the first Liga game to take place in the United States but was instead played at Villarreal's home after the league's organising body lost a legal battle with the Spanish soccer federation.
Villarreal played the more exciting football and also had several chances to break the deadlock, the best of which fell to Samuel Chukwueze who missed the target from inside the area.
Simeone's side began the season by winning their opening three games but have only managed to pick up two victories in their last 10 league games, form which seriously endangers their status as Spain's third force behind Barca and Real.
"The team kept on trying today but recently we are having no luck in front of goal," said Atletico midfielder Koke.
"You win matches by scoring and recently we have been finding it far harder than usual.
"We all need to reset ourselves and take a step forward so we can turn this situation around."
Villarreal, without a win in six league games, are 12th on 19 points.
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