Erik Ten Hag's ended eighth in the Premier League this season - their worst top-flight finish for 34 years.
However, they could still qualify for next season's Europa League if they upset the odds and deprive City of a second successive domestic double at Wembley.
"I think for a club like Manchester United to miss out on European football is hard to take," former defender Gary Pallister said in an interview with BetVictor.
"For years, we haven't missed out on Champions League football. Now, to miss out on Europe altogether would be a travesty."
Not being in Europe next season would be a serious blow to the record 20-times English champions' reputation, have financial consequences, and would not help them attract the kind of players required for a major squad re-building.
United lost to City in last year's FA Cup final and were beaten convincingly by Pep Guardiola's side in both Premier League clashes this season.
City are unbeaten in open play in all competitions since December and will be huge favourites in the showpiece.
"You've got to believe that you can compete with this Manchester City side," Pallister said.
"You need everybody to be firing on all cylinders - use the fact that you are the underdogs to your advantage and have that spirit that you can prove people wrong."
Three-times European champions United last missed out on Europe when they finished seventh in the 2013/14 season under David Moyes. The previous occasion was in 1990.
Should they win the Cup for the 13th time, it would mean Newcastle United, who finished seventh, missing out on the Europa Conference League.
