West Ham manager
Bilic felt his team were doubly wronged when Algerian Feghouli was harshly sent off for a 50-50 challenge with United's Phil Jones just 15 minutes into a 2-0 defeat against Jose Mourinho's side on Monday – which also featured a goal from Zlatan Ibrahimovic which looked suspiciously offside after Juan Mata had opened the scoring.
"Of course the sending off had a major impact on the game," said the Croatian coach whose side played 75 minutes with ten men.
"I was very surprised by it. I wouldn't even be happy with yellow because they both went in for the ball. Then I saw the replay and it was proof I'm right.
"The more times I see it, it was the other way around – it was Jones who made the more dangerous tackle. Definitely not a red card.
"We will appeal of course and I'm expecting at least to win the appeal. I will be extremely gutted if we have to lose him for three games. But I don't blame the referee personally. I can be angry during the game but I know it's not deliberate."
Bilic, however, refused to call for video technology to prevent similar mistakes occurring in future.
"I don't want to call for replays. Goal-line technology is brilliant, but the others I'm not sure - I'm still a little bit old fashioned even though I'm on the wrong side of it this time.
"But it's frustrating when your whole season, your job, could depend on one or two decisions – because the second goal is clearly offside too."
Bilic, whose West Ham team finished seventh in the Premier League last season but are only seven points clear of the relegation zone this time, now faces a battle to hang on to star names, not least France international Dimitri Payet.
He insisted: "We said it at the start of the season, that we are moving up and moving forward. We want to keep our best players and he is definitely our best player."
-- Six straight wins --
Meanwhile, Jose Mourinho is refusing to talk up a title bid even though his team have won six league games in a row and face Liverpool next at Old Trafford.
The result at the London Stadium leaves his team level on points with fifth-placed Tottenham, who play Chelsea at White Hart Lane on Wednesday, and only one point behind Arsenal, who are at Bournemouth on Tuesday.
"I think we can win the next match," Mourinho said when asked about United's ambitions.
"I prefer to be pragmatic this way. And after tomorrow Chelsea against Tottenham, one team loses or both drop two points. So we go step by step, we try to win our matches."
It was only the arrival of Mata at half-time and Marcus Rashford later which secured three points on a night when Dean's performance was the main focus of attention.
"I think we deserved to win but I have to be honest it was not a very good performance," admitted Mourinho.
"It is very difficult to play football in those circumstances, two games in 48 hours."
Next up for United is an FA Cup third round tie against Reading at the weekend followed by the first leg of an EFL Cup semi-final against Hull City - two opportunities for silverware in Mourinho's first season.
But the Premier League clash against Liverpool on January 15 could provide a better barometer of their ambition.