Having kicked off Group F with a shock late defeat at Young Boys, the Red Devils were facing the prospect of a third straight home defeat in all competitions after Paco Alcacer deservedly put the visitors ahead.
De Gea had prevented the opener coming sooner with some outstanding saves to deny Villarreal, against whom he missed the crucial penalty against in the Europa League final loss in Gdansk back in May.
Villarreal boss Unai Emery was proud of his side’s display in the defeat at Old Trafford.
“I think when you look back you kind of have to separate and make a contrast between the final result and the feelings that you get about how well we played,” the ex-Arsenal boss said.
“If you look at the game apart from the result you detect a certain pride, the desire, the way we used our football to transmit a feeling of hard work.
“We had a lot of possession of the ball, but unfortunately it’s a results game.”