The former Everton and Manchester United manager had warned that the away game would be his biggest test yet in Spain and his players failed to rise to the challenge.
"It could have been even worse as we committed serious mistakes," Moyes told a news conference.
"I think our opponents were better than us and they deserved the win. In the first half we were better but it was not good enough. We were up against a strong rival and we needed to be more solid."
The fact they held Villarreal at bay until the 64th minute, when keeper Enaut Zubikarai deflected in a Bruno Soriano free-kick after it came back off the bar, was mainly down to poor finishing.
Denis Cheryshev added another for Villarreal before a late double from Moi Gomez completed a dominant performance that leaves Sociedad three points off the drop zone in 14th position.
It is one place better than when Moyes arrived last month, with the team having picked up a point away to Deportivo la Coruna and beaten Elche so far in La Liga as well as drawing away to lower league Oviedo in the King’s Cup.
There have been some positive signs and Sunday was the first time they had conceded a goal but the difference in quality against Villarreal showed that Moyes has a long way to go to achieve his target of a European place.
"The attitude of the players has been good but the problem has been when we have had the ball and we have to compete better," said Moyes.
"It’s not the right time at the moment to talk about bringing players in. I need to time to consider who we have here and then think about the winter transfer window."
(Editing by Alan Baldwin)
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