The competition, which United have won 11 times but not since 2004, represents the final chance of a trophy in what has been a disappointing season for the Old Trafford club.
The last time they claimed silverware of any kind was in 2013, and Red Devils midfielder Herrera - who joined in 2014 - told MUTV: "We realise how important it is for us as players and for our fans to get a trophy
"I know how important the FA Cup is for our fans, and we don't have players in the dressing room who have won it for United.
"I was talking to (United midfielder) Michael Carrick about it and he told me he wants to win and get to Wembley."
The likes of Carrick, United playmaker Juan Mata and boss Louis van Gaal have also spoken since the 3-0 loss at Tottenham at the weekend about the magnitude of Wednesday's contest.
Certainly, victory at Upton Park - setting up a semi-final clash at Wembley with Everton - would provide a timely boost for Van Gaal and his men three days on from the Barclays Premier League defeat at White Hart Lane.
That game saw them collapse in alarming fashion in the second half, conceding three times in six minutes, and left fifth-placed United four points behind fourth-placed Manchester City in the table with each having six league fixtures to go.
It has prompted fresh questions over Van Gaal's future, while there have been reports of dressing-room unrest, with some players growing increasingly frustrated with the Dutchman.
In that context, it is notable that Herrera has emphasised the importance of the team showing "spirit" on Wednesday.
"The FA Cup is a big competition. It's very emotional," the 26-year-old Spaniard said.
"In the Premier League you show your balance (in terms of consistency over a season) but in the cup you show your spirit and your desire to win."
Herrera has also made it clear how excited he is personally by the prospect of playing at Wembley, although he has every expectation West Ham - who are sixth in the Premier League, led in the original tie that ended 1-1 and also drew 0-0 at Old Trafford in December - will prove tough to get past.
"If we beat West Ham we'll have the chance to play at Wembley, which is a fantastic stadium," Herrera said.
"I have a lot of things in mind about being there and we have a big chance to be there - but of course West Ham away is not easy."
United captain Wayne Rooney could make his first-team return in Wednesday's game.
The forward played 61 minutes for United's Under-21s on Monday in his first outing since sustaining a knee injury in February.
Source: PA