The Seagulls held a two goal advantage at half-time thanks to a Glenn Murray double, but second-half goals from Fulham's Calum Chambers, captain Aleksandar Mitrovic (two), and Luciano Vietto saw the home side complete a remarkable comeback.
Brighton have now picked up just five points in their last nine Premier League games and have yet to pick up a league win in 2019.
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After the game, Hughton was left angry by his side's second-half capitulation, and rued an usually poor defensive performance.
Here are the key points from the Brighton boss' post-match press conference:
A game of two halves:
"I thought for as good as we were in the first-half period, and I thought we were really good, it was as poor as what we were in the second-half period.
"What they did do was change the shape of the team early. Even in the first-half they changed the shape of the team to see if they could get themselves in more advanced positions and you have to be able to cope with that.
"We found it difficult to cope with it. We allowed them to get into too many areas that could potentially hurt us.
"In a game where I thought we certainly had good chances as what they did, we conceded poor goals and if you put all of them together it doesn't allow us to get a result."
Uncharacteristic Brighton defending:
"They were up against good players. Mitrovic is a very good player, and Vietto comes on along with Cairney and they got a lot of crosses in.
"Centre-halves also need support. If I'm looking at the first goal we allow a player to strike from the edge of the box and what that does do is give them a bit of momentum.
"Certainly the second goal gives them even more so. I thought we had chances when Fulham were 2-1 down.
"We get that third goal and maybe it becomes harder and it knocks them off their stride a little bit.
"Looking at the four goals we conceded they are four poor goals which is not like us. Particularly the form that we are in to concede four goals we haven't done that against the top teams.
"We found it hard to cope in that second-half. We needed to work harder at it."
Half-time turns game on its head:
"What I do think is that with their change in formation and the way that they were going about the play, they were going to have more possession. We had to work harder on the defensive side of our game.
"The first-half period, where we've got the momentum, we didn't allow that to happen. All the things we said at half-time was all about making sure that didn't happen.
"We didn't work hard enough in the areas that we needed to work hard in and we didn't give the back four the support that they needed."
Hughton gives hair-dryer:
"Of course I was angry with the team. From 2-0 up in a game where we're comfortable we conceded four goals in one half.
"Yes I was angry and the anger that I had I was certainly entitled to have. It was not like us that second-half period.
"Even in a game where you know you're going to concede possession and think 'you know what they're going for it', you still don't expect to concede four goals. That's not us.
"Playing top-six teams, where they're going to have 70, 80 per cent possession against us, we haven't conceded four goals so yes I was angry."
'Very good' first-half adds to disappointment:
"I didn't think we were good first-half, I thought we were very good in the first-half period. Apart from the two goals, I think Glenn has had a really good chance in that first-half. I thought we were really good.
"Perhaps we played a little bit deeper, and we should have changed the shape at times to get a little bit more pressure on the ball but that didn't allow us to stop the opportunities they had."
Poor decisions play part in downfall?:
"The second goal which came from the second phase on a corner, I never thought was a corner. The referee thought that Maty Ryan touched it over the top and certainly from where I was it looked like he didn't.
"There are probably some details that affected maybe the goals, but probably at this moment it's more about disappointment in our second-half performance."
Reaction needed to break slump:
"It's a must. This is not new to us. Our level of team in this division means we are going to have ups and downs and we're going to have setbacks and it's about how we react.
"Generally over this period of time we've reacted well enough on enough occasions to do OK. We're going to have to make sure that we do that again."
New faces in at the Amex?:
"At this moment, you never say no. If you had to ask my opinion, no our business is done."