West Ham lost 2-1 to the Red Devils in a quarter-final replay at Upton Park earlier in the season, after failing to find their best form in the contest.
Prior to the tie, Bilic had gone on record to suggest that he would have rather won the FA Cup than finished in the top four, but West Ham were unable to progress to Wembley.
Marcus Rashford and Marouane Fellaini scored United’s goals, and even though James Tomkins netted an equaliser it was not enough.
Bilic feels that the result was the worst moment of West Ham’s season, with defeats against Leicester City and Stoke City also being cited as frustrating ones.
“There haven’t been many,” Bilic responded, when asked what the worst moment of West Ham’s season was.
“Losing vs Leicester was a blow, but no one then knew that they would achieve. Since then few teams were able to put them under the same pressure.
“The last game defeat at Stoke was frustrating, but maybe the lowest point was the FA Cup defeat at home to Manchester United - our plans was to win the competition.”
There have not been too many poor results for West Ham over the course of the season, as they have put together an impressive campaign.
The Hammers are guaranteed to finish in the top seven, which represents excellent progress in Bilic’s first season in charge.