United, in sixth place, can also qualify for the Europa League by beating Crystal Palace in the FA Cup final on Saturday.
If they do so, a Europa League spot will become available for the team finishing seventh in the Premier League.
"It is very frustrating. For most of the season we have been there (in the Europa League qualification spot) and it looked like we were going to do it but the competition is really good," Bilic told British media.
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"Overall it was a great season and we hope Man United win the FA Cup and then we will be in the qualification for the Europa League.
"There are many good teams, but of course we are not happy that we lost the position over the last three or four games."
West Ham qualified for last season's Europa League by winning the Premier League's fair play table, but lost to Romanian side FC Astra Giurgiu in the third qualifying round.
(Reporting by Nivedita Shankar in Bengaluru, editing by Ed Osmond)
