The Seagulls can secure their fate with two games to spare with a win over the Red Devils at the AMEX on Friday night.
But they got the helping hand they needed from the goal line technology system to seal another campaign in the Premier League on 57 minutes.
"They clearly showed that, for them, it's more important for them to stay in the Premier League than for us to finish second".
"Overall, attitude during the first half they were obviously stronger than us with more appetite, they felt it with different emotions", Mourinho said of Brighton's energetic performance.
"I wouldn't say disappointed".
"If we manage to finish second it's more than great".
The team from the south coast are eight points clear of 18-place Southampton and 17-place Swansea.
The defeat leaves Manchester United second place in the Premier League table, five points clear of third-place Liverpool in the race for second-place. It wasn't the fact that they played badly, it was that their attitude was awful. Maybe now you understand why some players don't play more than others. Why this player is on the bench? Why always Lukaku? Why always Lukaku?. you have the answer 'why always Lukaku'. "Why always Lukaku? Why also Lukaku?'", said Jose Mourinho in the aftermath of his side's defeat.
Mourinho tore into his players after the match and Neville believes the performance on Friday night proved that several members of the squad have stopped playing for their manager.
Belgium worldwide Lukaku has played the entire 90 minutes in 30 Premier League games this season, scoring 16 times.
But Brighton held on, meaning United have been beaten by all three promoted sides - having lost at Huddersfield Town and Newcastle United - in the same Premier League season for the first time.
Many of United's most talented attacking outlets this season have been stifled this season by Jose Mourinho's more conservative tactics, with Pogba, Martial and more recently Alexis Sanchez suffering.