Jadon Sancho has been banished from the first-team squad and Antony given a leave of absence following assault allegations against him which the player denies since the galling, last-gasp loss at Arsenal.
Brighton heaped further misery on United as attention returned to on-field matters on Saturday afternoon, with Danny Welbeck, Pascal Gross and Joao Pedro scoring before Hannibal Mejbri’s consolation effort.
The comprehensive end of the Red Devils’ 31-game unbeaten home run in all competitions came against the side that last beat them in the league at Old Trafford in Ten Hag’s first match in charge.
Gross netted both goals in last season’s Old Trafford win and fired Roberto De Zerbi’s men further ahead early in the second half, before substitute Pedro landed another body blow.
Boos greeted Ten Hag’s decision to bring Anthony Martial on for full debutant Hojlund, but fellow introduction Hannibal did his bit when striking home his first for the club from distance.
Brighton have a historic Europa League match against AEK Athens to look forward to themselves after winning at Old Trafford for just the second time in their history.
De Zerbi surprisingly made six changes on Saturday, when Ten Hag made three and plumped for a midfield diamond that caused the visitors early problems.
Rashford’s skill and perseverance ended with a low drive being saved by Jason Steele and Hojlund headed over, before nearly combining when the new boy stretched for the homegrown star’s cross.
But De Zerbi’s side looked unruffled and took a 20th-minute lead at the end of a well-worked move.
The opener gave Brighton fans an extra pep in the step and the goalscorer tried his luck from distance, with United offering little in response until the 34th minute.
Casemiro swept the ball out to Rashford on the left, with the forward darting inside and getting away a drive that Joel Veltman turned onto the woodwork with an unorthodox block.
United bounced back from that near miss and celebrated an equaliser five minutes before the break.
Rashford followed stepovers by darting to the byline and pulling back for Hojlund, who turned and prodded in what appeared to be his first United goal.
But with play ready to resume at 1-1, referee Jarred Gillett was informed by VAR Chris Kavanagh that the ball had gone out of play before Rashford could get the pass away.
The England international continued to look dangerous and went close in stoppage time, then struck into the side-netting when the second half got under way.
But Brighton were still pursuing a second and their warning shots across the bows went unheeded.
The 53rd-minute effort left United reeling and Ten Hag turned to his bench, but the decision to replace Hojlund with Martial was audibly unpopular.
Rashford saw a free-kick stopped as the hosts desperately looked to claw a goal back, only to be hit by a Brighton third in the 71st minute.
Lamptey raced down the left and cut back for substitute Pedro, who opened his body to hit a first-time, right-footed shot that Onana could not stop finding the net.
Punch-drunk United managed to pull one back immediately through youngster Hannibal, who lasered an effort past Steele from 25 yards two minutes later.
Victor Lindelof headed over but intelligent Brighton were able to take the sting out of proceedings, exposing gaps left by the desperate hosts.