In the post-match interview, Marcus Rashford told BT Sport: "The feeling inside is difficult to explain.
"We came here to win. We've been working so hard all season and this was the opportunity to win a trophy and it didn't happen for whatever reason.
"We have to get rid of the disappointment and look back at the game and see what we did wrong. The team will not give up - no chance. The manager won't allow us to give up. We will come next season with bigger desire.
"People say a lot about Man United going downhill, blah, blah, blah, blah but for me, the club, desire, hunger, talent, ability, the squad, we have everything to compete at the highest level.
"We just have to show it to the world and ourselves, show why we belong in the top places and why we need to win finals like this.
"Second doesn't count for nothing. Manchester City win the league, we finished second. Doesn't mean nothing. Villarreal won the Europa League, we finished second.
"For us it's nothing. I don't want to hear 'they were so close' because it means nothing. One winner, one loser. Today we lost. We have to find out why and make sure next time we don't lose."
Rashford missed a couple of great opportunities to score during the game but he nailed his penalty in the intense shootout that followed.
He was in tears after the Red Devils lost the trophy but it's important to hold our heads high and move on.
