Edinson Cavani levelled during a bright start to the second half, but that soon petered out and the match ended 1-1 after extra time with David De Gea's saved spot-kick seeing Villarreal triumph 11-10.

"I always believe in our players and I thought we did what we needed to and pushed on for about five to 10 minutes after equalising," Solskjaer said.

"But then when the goal didn't come on, we couldn't kick onto the next level.

"To be honest, I felt we probably more and more dropped off as the game wore on.

"Of course it's very, very disappointing. It's hard, there's loads of disappointment in the dressing room but in a penalty shootout anything can happen.

"I thought the penalties were really of a high standard so can't fault the focus."

Asked about the hurt of such a challenging campaign ending like this, Solskjaer said: "You've got to be strong.

"You've got to learn from failure, learn from these disappointments because it's a lesson.

"It's a lesson that we're still not where we want to be, still not at the quality we want to be.

"We go away now – some in the Euros, some have holidays.

"The one thing that's definite is that everyone has to come back with a desire to improve.

"I'm sure that they'll have this feeling for a couple of days and then come back stronger."

De Gea is among those heading to the Euros and will feel that disappointment more than most, having failed to save any of Villarreal's 11 spot-kicks before seeing his key strike saved by Geronimo Rulli.

"Of course disappointed as all of us (are) but that's football," Solskjaer told MUTV.

"Sometimes you're the hero, sometimes it doesn't work for you and I'm sure he'll survive this one."

Solskjaer has an interesting call to make on his goalkeepers this summer, having juggled the playing time of Dean Henderson and De Gea across the campaign.

The latter got the nod for the Europa League final but is a notoriously poor penalty shot-stopper, conceding the last 40 spot-kicks he has faced for club and country.

"You go through every scenario, of course, and it has crossed my mind in the build-up to the game," Solskjaer said when asked if he had considered putting Henderson in for the shootout.

"But we were confident in David and we'd prepared.

"But penalties, anything can happen in those. I stuck with the keeper who played all the game."

It will be one of a number of decisions Solskjaer will pore over in the coming weeks and months, so too will be his call not to make any changes to his stuttering side until the 100th minute.

"Well, we felt the players out there, you got Mason (Greenwood), Marcus (Rashford) who are match-winners in their own right. Bruno (Fernandes), Edi, of course they can create anything," the Norwegian added.

"Scott (McTominay) I thought was the best player on the pitch and Paul (Pogba), so it's difficult to make that change, especially when Fred's been injured for a week.

"He came on and he did well, the boy. We just couldn't create enough chances to win the game.

"When they've got (Pau) Torres and (Raul) Albiol in there with crosses it's always going to be difficult. We needed to play our way into the box quicker."