Since I'm not neither a United or Villarreal fan (I was rooting for the later as a Spanish club) I think I can give you a different point of view.
I've read many times that United deserved the win because "we tried", that Villarreal were "antifootball".
To me, the draw was a fair result.
From my point of view United didn't try more than Villarreal, United only had more possession (and as a Barça fan I know what I'm talking about).
How many chances did you create? 0 real clear chances. Even the goal was a fluke with a few rebounds.
Villarreal didn't create any, but their goal was "legit" (in terms of just strategy and not a few unlucky rebounds).
Very similar stats (similar number of shots, Villarreal more than doubling in corners...), only difference was possession. Not enough to me to determine that United deserved more.
The good thing about Villarreal is that they can wear many suits. They can manage the game from the possession but they can also do it from the defense.
Manchester is a great team with open spaces, fast transitions, with fast players, but it is pretty average (when compared to top European clubs) when they need to dominate and break a close defense. United struggles a lot when spaces are hard to find.
Villarreal played the match that gave them more probabilities to win. You would probably prefer a team like Real Sociedad that plays open and leave spaces... not very smart if you want to win United with a worse squad.
One thing is to park the bus ALWAYS, concede 25 shots and try to score one of your 2 shots and a different story is playing to minimize the virtues of your (superior) rival and level the number of chances you have at the end of the game.
Villarreal played "a final" to get a Europa League spot (they ended up 7th in Conference Cup spot) last weekend against Real Madrid (Real Madrid scored in the 88' and 94' for a 2-1 win). Real Madrid also struggles with close defenses. But Villarreal also "played the Europa League final"... it was a test of what they were going to try today. In fact, the squad was basically the same. Many people thought they were crazy because "they are going to be tired against United". It ended up to be the opposite, Villarreal tested the game plan and they were able to dominate the extra time. They needed to play two difficult and important games in 4 days, so they needed a game plan that could work in term of tactics and in term of outcome probabilities.
It is not beautiful... but this is a European final, a spot in the Champions League was on the line for Villarreal too... their 1st European title... it was pretty obvious that Villarreal was going to try to sit tight and counter attack. This is not a random league game. Things are different in finals.
That is the reason I think Ole had an awful lecture of the game... you are not going to have spaces, you will need less speed and more creativity. You can save some speed for the moment the game breaks, or the last minutes... you need more "Matas" (or that kind of player) and less "Rashfords" that lose 90% of their powers when they cannot run. You don't want a Ferrari to race a rally.
Emery won the final to Ole. DDG is just another victim.
Anyway, I think United is progressing and going in the right direction.