The Hammers boss says his side have more confidence than United and the prospect of last-ever cup tie at Upton Park will only add extra incentive.
Anthony Martial struck a late equaliser to deny the Hammers a semi-final place at Wembley after Dimitri Payet's stunning free-kick had given the visitors the lead at Old Trafford on Sunday.
That leveller forced a replay which will serve as the last-ever cup tie at Upton Park before the Irons take up residency in the Olympic Stadium from the start of next season.
Bilic insists that, as well as the confidence his side have from enjoying such a fine season, the prospect of a last, glorious knockout match at the club's traditional home will give his side a crucial upper hand in the rematch.
The Croatian boss told BBC Sport: "It's going to be a tough game, but I fancy us because we're going to be even more confident. Manchester United are a different team when they play away from home and don't have that same confidence.
"With the history of our stadium it's going to a be another historic game and you can't ask for more, but to make history we have to beat them - we won't put it in the books if we lose the last game.
"It's going to be another epic home FA Cup match and we couldn't ask for more - it's like [a Steven] Spielberg [film]."
Victory over Louis van Gaal's side to book a Wembley date would be another highlight of an already memorable final season at the Boleyn Ground for the Irons.
In Bilic's first season since taking over from Sam Allardyce in the summer, the Hammers sit fifth in the Premier League table, in a guaranteed Europa League spot and just two points off a place in the top four with nine matches of the season remaining.
There has been plenty for the Upton Park crowd to cheer throughout the campaign, as the London side have not lost in front of their own fans in any competition since August, a run stretching 14 matches.
With the date of the replay against the Red Devils still unknown, West Ham must now turn their attention back to a defining run in the league, as they face Chelsea, Arsenal, and Leicester City in three of their next four matches.