Villarreal coach Manuel Pellegrini said his side deserved to win by a bigger margin over Celtic in their group E match in Spain.
Marcos Senna scored from a second-half direct free-kick to leave the Scottish side with one point from two games.
"I don't think the scoreboard reflected the way we dominated the game," said the Chilean.
"They obviously came for a result but didn't get what they wanted, and didn't do a lot in our side of the pitch."
Celtic coach Gordon Strachan said he thought the decision to award the foul for Senna's goal was dubious.
But Pellegrini was non-committal saying: "I don't know if it was a foul, I don't remember, but the referee gave it so it was a foul."
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