United fell behind to Moises Caicedo's first-half strike before Marc Cucurella, Pascal Gross, and Leandro Trossard scored second-half goals to condemn the Red Devils to a humiliating defeat at Amex Stadium.
They have now conceded more league goals this season (56) than in any other Premier League campaign, and with 58 points after 37 games, United is guaranteed to record its lowest points tally in the competition, setting a new low from the previously held record of 64 points in 2013-2014.
United has now conceded four or more goals in 12 separate Premier League games since Sir Alex Ferguson retired in 2013, as many times as it did in 810 games under him in the competition.
Speaking after United's fifth consecutive away league defeat, Rangnick rejected the idea that his players had "ignored" his game plan but called the defeat "humiliating".
Asked whether the loss was the worst he had experienced since arriving at Old Trafford, Rangnick replied: "It was. From the first to the last minute this was just not enough, in all important areas we were second best and we can only apologise to our supporters.
"It was a terrible performance and a humiliating defeat. Today, from the first minute we gave them too much time, too much space, we were never in a position where we could stop them playing through our lines.
"I don't think that they ignored the game plan, but we were just not able to stop them, we gave them too much time and space and if you do that against a technically good team like Brighton, this is the result."
The Seagulls' comprehensive victory represented the biggest top-flight win in their history, in what was their 365th game at this level.
Rangnick attempted to change the game at the break by introducing Edinson Cavani and Fred, and despite three of Brighton's four goals arriving in the second period, maintained something had to change after United failed to register a shot on target in the first half.
"As I said, it was very, very difficult in the first half to stop them at all. In the second half we took the risk to bring on Edinson as a second striker plus Fred, and play 4-4-2", he added.
"In hindsight, maybe it was too much of a risk to play in a 4-4-2 against them but we had to change the energy, today we were just second best in all relevant areas.
"Had we continued to play as we did in the first half it would only have been a question of time when we conceded the second goal, that's why I decided to take more of a risk with the 4-4-2. But with two early goals, it was a disaster for us. As a team, we didn't defend at all."
Rangnick now has just one match left in the Old Trafford dugout, with United rounding off their frustrating season with a final-day trip to Crystal Palace before Erik ten Hag takes charge.
Looking back on his tenure at United, Rangnick who will assume a consultancy position after vacating his coaching role, claims his side was "on the right pathway" for much of his time in charge, though admitted the Red Devils have been "really poor" recently.
"I think we have to split it into two different halves. Until the West Ham [United] game [a 1-0 win in late January] or even the Tottenham [Hotspur] game [a 3-2 victory in March], we had very good performances, when we beat Tottenham at home, West Ham at home, when we won [4-2] at Leeds [United], it was a completely different level of energy.
"But in games like today, or at Everton [a 1-0 defeat last month], it was a lack of energy, of aggressiveness. If you play like that without the ball you cannot win a game.
"When the call came in November it was clear I wanted to come, and as I said, in the first three or four months we were on the right pathway, we were in three competitions and had really good performances, but in the last four, five, six weeks, we were really poor."