Mikel Arteta's side came into this game knowing they needed to overturn a 2-1 deficit in the semi-final.
Having been named in the original starting lineup, Swiss midfielder Granit Xhaka missed out on the game due to a knock he picked up in the pre-match warm-up.
Replacing Xhaka at left-back was Kieran Tierney, who played his first game since returning from a short spell out. Arteta would have had to assess the situation quickly, as the Scotsman remains a key member of the side - losing him to injury again before the final would have been detrimental.
The game started fairly cautiously from both sides, but Villarreal winger Samuel Chukwueze went close in the opening stages, as he bent a left-footed strike towards the back post, forcing a smart save from goalkeeper Bernd Leno.
Arsenal began to dominate the right areas of the pitch in the first 20 minutes of the tie, but they were consistently lacking the final ball to put them into scoring positions.
Thomas Partey conceded a free-kick in a dangerous area in the 23rd minute for midfielder Dani Parejo to place just over the crossbar - the warning signs were there for the Gunners that Unai Emery's side weren't there to solely defend their lead.
Arsenal captain Pierre-Emerick Aubameyang came inches from putting the North London side in the lead as he latched on to a loose ball, striking with the outside of his foot onto the outside of the left post.
We should never wish an injury upon any player, but it would be a understatement to say that Gunners fans were relieved when Chukwueze was stretchered off in the 29th minute - over the two ties, he had looked far and away Villarreal's most dangerous player.
Aubameyang went close again towards the end of the first half, as he picked up the ball in his favoured position on the left-hand side, striking towards the back post and almost beating goalkeeper Geronimo Rulli with the power of the strike.
The first half ended goalless, with the home side having the better of the chances - Arteta's side grew into the game as it went on, but struggled to really hit top gear before the break.
Nicolas Pepe, had a good chance to give Arsenal the lead in the opening moments of the second half, as he struck wide and right of the goal having been played through in an exciting build-up.
Just minutes after, Emile Smith-Rowe went even closer as he picked up a loose header, and with the goalkeeper floundering he 'dinked' the ball just wide.
Arsenal had seemingly come out of the break inspired by their managers words - displaying a level of intensity that they were assuredly missing in the first half.
A couple of nervy moments will have made Arsenal fans take in a few sharp breaths, as alongside their attacking impetus came a number of sloppy mistakes.
The second half continued to present half-chances for both sides, but with no real clear-cut opportunities, the game quickly moved into the final 20 minutes.
In the 72nd minute, centre-back Rob Holding glanced a header just wide of the post, having got on the end of an immaculate cross from Smith-Rowe.
Captain Aubameyang hit the post again in the 78th minute, having beaten off two Villarreal defenders to win the ball in the air - it began to get desperate in the closing stages of the game.
Hector Bellerin was unlucky not to put away one of the two chances he had inside 30 seconds, with two vital blocks vanquishing his opportunities.
Just not good enough
In spite of the chances they had, the Gunners failed to find their winning goal, sending them crashing out of the Europa League at the hands of their former manager. A painful moment for all associated with the club.
With little to look forward to for the rest of the season, many questions will be asked of Arteta and his squad as they face a tough few months ahead in the wake of this loss.