Villarreal is indeed a strong team, but they are no better than Barcelona, in this match I did not see that Villarreal played well, but it was Barcelona who played badly so they could concede 3 goals even when Barcelona was 2-0 up. Villarreal was able to turn things around, until finally Barcelona's players came back to make the game 4--3 but it will be another evaluation for Xavi to continue to improve this team before facing more difficult opponents.
And what is of great concern is Barcelona's bottom line this season, look at how bad Barcelona's defense is, this is a pretty serious issue if Barcelona faces a tougher team, maybe to compete in La Liga Barcelona is still quite calculated but I really don't sure they will be able to compete tightly in the UCL stage.
Yes, that's right, Villareal are a good team but of course not better than Barcelona. And it's true that as you said Barcelona didn't play well especially in the defensive area. Barcelona's defense must be repaired immediately otherwise Barcelona will find it difficult to face strong teams like Atletico Madrid and Real Madrid.
In that match, it was clear that Barcelona's defense that was not good was Sergi Roberto. Because of Villareal's first goal, instead of heading the ball, he just watched, and also during Villareal's second goal, he couldn't cut the ball on the right. And Villarreal's third also came from Roberto's position and he was slow to come down.
For me, even though a top club like Barca certainly has weaknesses when they meet certain club and even though it looks convincing when Barca plays Villarreal, it not guarantee that Barca can beat it because we know that sometimes a club performance suddenly drops and sometimes there is carelessness on the defense and for me this is normal because problems like this happen to other club too.
But even though Barca lost, I think Barcelona has performed very well because Villarreal are lucky be able to beat Barca with only 1 score difference and this is not serious problem for Barca defense line and I think all of this can be fixed because I believe Xavi is able to increase.