The Red Devils appeared ready to challenge for the top-flight crown having burst out of the blocks in 2017-18 amid a flurry of goals and clean sheets.
Jose Mourinho’s side were unable to maintain those levels, though, and were forced to watch on helplessly as arch-rivals Manchester City swept to 100 points in a record-breaking campaign.
United can secure the consolation prize of major silverware at Wembley on Saturday when they take on Chelsea, but Young admits everyone associated with the club is hoping for more in 2018-19.
The England international told MUTV: "If we win at the weekend, and finishing second, it will be a very good campaign but, if you ask all the players and staff, winning the league is where we need to be at. I think that's the disappointment but, overall, I think it's been a good season and, if we win the FA Cup, it's been a very good season.
"Of course there's excitement [for the final]. There is not anyone who is not excited. We've been there before and must prepare this week in the right way, which we will do. Everybody is wanting to be starting, wanting to play, and I'm no different.
"I want to play in the FA Cup final and obviously want success. There is no better feeling than when you win the FA Cup and walk up those stairs to pick up that trophy. Hopefully, we can do that."
Young is also waiting on the announcement of England’s preliminary squad for World Cup 2018, with Gareth Southgate set to reveal his selection on Wednesday.
The versatile 32-year-old could get the nod, with an experienced performer at Old Trafford having reinvented himself this season as a hard-working left-back.
"It's been a massive boost for me, playing week in and week out," said Young.
"I'm playing in a new position and feel like I can adapt. I've got a good footballing brain. I know where to be on the pitch and when to attack and when to defend.
"I've enjoyed the season and it's gone even better than I had thought as I've got myself back in the England squad. Fingers crossed for when the squad is announced, hopefully that would be an achievement in itself.”