David Moyes' side host Sunderland in the second leg of their semi-final on Wednesday night, looking to overturn a 2-1 deficit from the first leg at the Stadium of Light.
United were also beaten at the weekend, 3-1 by Chelsea in the Premier League at Stamford Bridge, and Neville believes it is important his former club bounces back in another big game.
He told Sky Sports: "It's a big game for two reasons. Firstly, it's the immediate game (after Chelsea), but secondly Manchester United and David Moyes need to get a trophy under their belt.
"I think the club at the moment needs a big-game win. If you're looking at this moment in time to salvage something out of this season they've got the Champions League to look forward to, if they can win on Wednesday night they've got a cup final - though City would be big favourites - and then obviously they've got to try and get fourth spot.
"I think in terms of realistic achievements this is a big part of it. To go out against Sunderland on Wednesday would be another massive dent in this season."
Sunderland, despite sitting 19th in the Premier League, have been in reasonably good form of late, picking up four wins in their last seven games including the 2-1 first-leg win over United.
Neville believes Gus Poyet's side will have one aim, to score the first goal and build on the Old Trafford anxiety that has seen them lose five games in all competitions at home this season.
"Obviously Sunderland are going to be up for it because there's a carrot for them as well. Gus Poyet wants to get to a Cup Final and put more belief and confidence into his team," added Neville.
"The big thing for Sunderland will be to score a goal and to score the first goal. I'm sure they'll be concentrating on that because what that will then do is create nervousness in United's team.
"When they're 1-0 down it's been difficult for them at times at Old Trafford. You think about West Brom, Newcastle and against Everton, so actually getting that first goal must be the target that Gus Poyet is going for.
"I think he's got to go there and be aggressive, be positive and try and create a nervousness and anxiety that does exist when you're going through a bad period, which United obviously are."