The Red Devils announced on Tuesday that only 1,400 United fans will be present in the 51,000-seater De Kuip Stadium for the opening Group A fixture next Thursday.
The Dutch club were heavily punished by UEFA for crowd trouble during the Europa League tie with AS Roma last season. Hence, they have reduced the allocation to the away fans to avoid any repeat of the Roma game.
United had appealed to the UEFA against the ticket allocation, but their appeal was rejected on police advice.
A Manchester United Supporters' Trust statement to the Daily Mail read: "M.U.S.T and our travelling support are really disappointed about the reduced allocation for United supporters.
"We don't see why our fans should be affected by the Police concerns over home fans' behaviour and choosing to reduce their capacity for the match.
"We are glad United took this issue seriously and lobbied on our behalf, and M.U.S.T has also written to Dutch authorities seeking more answers, but sadly the short time frame between the draw and the match means we cannot change the outcome this time.
"We have also made the point that reducing the away allocation for such an easily accessible game may prove counter-productive and potentially increase security risk if ticketless MUFC fans are in the vicinity of the stadium attempting to get tickets."