Just after the hour mark, ten Hag made a double replacement with United behind by two goals.
Youngster Hannibal Mejbri took over for Casemiro, and Anthony Martial was added to the lineup to fill in for the international for Denmark.
Boos could be heard around Old Trafford as a result of the judgment, and United lost 3-1, their third defeat in their first five Premier League games.
Hojlund had been perhaps United’s finest player on a difficult home afternoon, but his first goal for the team was ruled out because Marcus Rashford’s cross was deemed to have left the pitch before it reached the striker.
The Atalanta player who cost £72 million was making his club debut after making his debut off the bench against Arsenal before the break.
After 20 minutes, former United striker Danny Welbeck gave Brighton the lead and eight minutes into the second half, Pascal Gross doubled it.
Ten Hag’s double substitution made things worse before Joao Pedro added a third goal.
Mejbri scored his first goal for the team after coming off the bench to restore parity.
However, Brighton maintained control of the game for the remainder, stopping Ansu Fati from scoring a fourth goal for the visitors. There was no more comeback.
United’s loss places them in 12th place with just six points from five games.
With an intimidating trip to Bayern Munich looming the next week, attention instantly turns to their opening Champions League group match.