Edinson Cavani levelled after Gerard Moreno had opened the scoring from a first-half free-kick in Poland, where the match ended 1-1 after extra-time and went to penalties.

All outfield players scored as did Villarreal goalkeeper Geronimo Rulli, who saved David De Gea's spot-kick to seal an epic 11-10 shootout triumph and send the yellow wall wild.

"That disappointment is the worst feeling," said United manager Solskjaer, who watched confetti rain down as fireworks filled the air when Villarreal lifted the trophy.

"These are the moments you remember the most in your career as a player, as a manager.

"There's two ways. You can feel sorry for yourself and go on holiday and don't do anything about it.

"Or you can go home and do something about it and come back even better, stronger, more hungry, ready from the first minute because we know that we didn't start this season great.

"We fell behind, too far behind to be challenging for the league so we need to start really well."

Solskjaer made some debatable decisions in the Europa League final, but the lack of elite strength in depth hampered his ability to change the game.

"I've been delighted with the effort, the desire, determination of all the players, you know, I can't fault them at all," the United manager said.

"We've probably done as well as anyone could imagine so, yeah, we who are here now need to do better.

"We need to work better, work harder, cleverer, but, as I've said, two or three players to strengthen the starting XI and the squad all together (is important).

"It's important for us to go even further because I'm sure our contenders or challengers will also challenge to improve so we want to improve as much as we can."

It was a painful end to a promising season for United, who finished runners-up to Manchester City as they secured back-to-back top-four finishes for the first time since Sir Alex Ferguson retired.

But Solskjaer knows that is not enough for the Old Trafford giants as they strive for more.

"No, it's not a successful season, of course, and that's the fine margins in football," he said.

"Sometimes one kick can define a season as a good one or a successful one, or one kick says it's not.

"Improvement, yeah. Second in the league, probably nobody expected us to be second in the league after the start we had, after the lack of pre-season we had.

"But the boys have been really, really good and just came up short tonight, unfortunately.

"That's on penalties. We could have been sat here saying it's been a successful season after the same game.

"But trophies matter and that's what matters at this club."

United forward Marcus Rashford promised United would bounce back strongly from the disappointment next season.

"We have to get rid of the disappointment and after that we need to look back at the game and see what we've done wrong and where we can improve," he told BT Sport.

"All I can say is the team will not give up, there is no chance this team gives up. The manager will not give up, he will not allow us to give up. We will come next season with a bigger desire.

"People say a lot about Manchester United, they are going downhill, blah blah blah.

"But, for me, the desire, the hunger, the talent, the ability of the squad – we have everything to compete at the highest level. We just have to show it to the world and show it to ourselves.

"Just because we lost today – I promise the fans we don't give up. There is no chance we give up. We are close but close is not good enough. We have to be there."

Villarreal had never won a major trophy until Wednesday's shock shootout triumph, but ex-Arsenal boss Unai Emery collected his fourth Europa League crown.

"I am very happy," the Spaniard said. "These players have worked very hard through the season, for the president, the owner, the chairman.

"We are very proud of Villarreal. I think we deserved to win.

"It was Manchester United but we played a very competitive match tonight."