It means the club will likely miss out on European football for the first time in 25 years.
And Keown thinks Arteta could be under the spotlight after a subpar performance in north London.
"I think just four (shots on target) in both ties," Keown said on BT Sport. "Villarreal controlled the tactics, Emery I thought was too smart for Arteta.
"Hugely disappointing, they were nervous, tentative, the performance wasn't there and we shouldn't be surprised, when we look at the Premier League position, ninth in the table, 19 goals scored here from 17 home matches.
"It's been a roller coaster season and inconsistency is rife through the group.
"I think the manager comes under enormous pressure. You start to look at the wisdom of a young manager coming here to take a huge job, a massive job at this football club.
"His inexperience, maybe, has cost him. He's still here as manager, we'll have to wait and see what happens on that.
"It seemed to me, though, that this was the rescue package tonight and it didn't arrive, the team didn't turn up, whether it was the motivation, the tactics - he was outsmarted by the previous manager which is also a bit of an embarrassment for the owners.
"Both games, the false nine and today when we changed our midfield completely and it looked like it was brand new to us, it didn't look like we had the experience to adapt, to change.
"We looked lost. They engaged us high up the pitch, we couldn't get out, we looked a bit nervy, and it allowed them to play and be comfortable.
"That's the thing, we haven't really laid a glove on them, we haven't gone down fighting. If this stadium was full, they wouldn't be allowed to get away with that.
"They almost seemed prepared to let the game glow away, I think it does come from the manager, he gives the tactics at the start, it's the base for the players to play from."