“It’s going to be a tough game, but I fancy us because we’re going to be even more confident,” Bilic told BBC Sport.
“Manchester United are a different team when they play away from home and don’t have that same confidence.”
West Ham are moving to the Olympic Stadium next season so the game against Manchester United will be the last at the Hammers’ current Upton Park home.
“With the history of our stadium it’s going to a be another historic game and you can’t ask for more,” added Bilic.
“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 Spielberg.”
Bilic unhappy at crucial decisions
West Ham had an appeal for a penalty rejected after Dimitri Payet appeared to be brought down by Marcos Rojo, but referee Martin Atkinson ignored the appeals.
Manchester United’s players believed Payet, who was already on a yellow card, had dived but no action was taken against him before he scored from a 40-yard free-kick minutes later.
“For me it is a penalty, Rojo slides from behind and is nowhere near the ball – a clear penalty,” said Bilic.
“When you are sliding in the box you are taking a big gamble and a big risk. Nobody in the world can say there wasn’t a touch. It is definitely not a dive.”
The Hammers boss was also unhappy that Manchester United’s equaliser, which was scored by Anthony Martial, was allowed to stand as midfielder Bastian Schweinsteiger appeared to block West Ham goalkeeper Darren Randolph.
“It is an obvious foul from Schweinsteiger on Randy,” added Bilic. “He would’ve definitely got to the ball.
“There were two crucial decisions but I don’t want to spoil the game by moaning about the referee.”
Manchester United’s ‘amazing spirit’
Manchester United boss Louis van Gaal refused to comment on the referee’s performance, but praised his side’s effort three days after playing on Thursday in their 2-0 loss to Liverpool in the first leg of their last-16 Europa League tie.
“The difference was that we have played a match on Thursday and they have the whole week of preparation,” said Van Gaal.
“In the second half we were the better team, they scored a free-kick, we are behind and have also played against WBA and Liverpool this week and lost.
“But when you can come back from that I think it is amazing spirit in the team in spite of a very nasty week.”
On the two controversial decisions by Atkinson, Van Gaal said: “We can discuss every decision of the referee but I only can say we are very unlucky this season with referees’ decisions.
“He has to decide within one second. That is more difficult than I can do.”
‘A perfect moment of pure class’
Hammers boss Bilic also praised Payet for his spectacular free-kick that gave the Hammers the lead.
“My assistants told me he scored a similar one in the warm-up,” said Bilic. “He also scored against Blackburn in the FA Cup and I said to myself: ‘It is a bit too far, it has got to be special.’
“It was a perfect moment of pure class and even David de Gea couldn’t do anything about it.”