The Seagulls are eighth in the Premier League, on 50 points with three matches remaining, as they seek European football for only the second time in the club's history.
Hurzeler, 33, had 12 months to run on his existing deal.
What do you make of the news? How do you rate Hurzeler's time in charge so far? And how far can he take you now?
'We've got three massive games to go'published at 11:44 BST
11:44 BST
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Jack Hinshelwood says he can "assure everyone" that he and his Brighton team-mates will "work so hard this week and show a reaction next Saturday".
Albion are eighth in the Premier League following their defeat at Newcastle and face Wolves next at the Amex (Saturday, 15:00 BST).
He told BBC Radio Sussex: "The support we've had at the Amex recently has been unbelievable. We're going to need that again come Saturday.
"We've got three massive games to go - all really important games. It's going to be an exciting end to the season.
"We can be disappointed [with the Newcastle defeat] but all focus has got to be on the next game and doing what we have been doing - getting back to the basics, training really hard and coming out firing next Saturday."
Sixth will earn a Europa League place at the very least, with some of the contenders having never qualified for Europe before.
However, both elements needed for sixth place to become a Champions League spot seem quite plausible.
Aston Villa would need to finish in fifth, exactly where they currently reside, and win the Europa League. They trail Nottingham Forest 1-0 after the semi-final first leg, but they are at home for Thursday's return leg.
This scenario will only play out if Villa finish fifth - and not in the top four or below fifth - because of a quirk in Uefa's rules.
The Premier League landed a fifth Champions League place because of the English teams' performances in Europe - something called the European Performance Spot (EPS).
So if Villa win the Europa League and finish fifth, that EPS spot would be passed down to the team in sixth, who would qualify for the Champions League.
However if Villa finish in the top four, winning the Europa League would make no difference to any other English team and the sixth-placed finisher would qualify for the Europa League.
With Aston Villa six points clear in fifth, sixth place appears to be the highest any of the other teams could finish.
At the moment, Bournemouth are on 52 points - one point clear of Brentford, who are one point above Brighton.
The Cherries and the Bees have never played in European competition before, while the Seagulls' only Uefa campaign was in the 2023-24 Europa League.
Chelsea are four points behind Bournemouth, but they have a game in hand against Forest.
Fulham are level on points with Chelsea. Everton, who have a game in hand against Manchester City, and Sunderland are on 47 points - so they are just about in the race.
Newcastle, Crystal Palace and Leeds could still mathematically - but not so realistically - qualify for the Champions League.
Wesley: I stick with Eddie Howe, but his tactics are puzzling sometimes. You need a team to play 90 minutes, not chop around in the second half. Hard to settle three subs into the game. Harvey Barnes should be on every game... all game.
Chris: Newcastle were a touch fortunate. Brighton dominated and maybe deserved a point.
JD: Thought the score was flattering to Newcastle. You can see why Osula is keeping the big-money strikers out of the starting XI. His running and pressing is relentless and he's unpredictable, which makes defenders nervous. It stopped Brighton's build from the back. Best player on the pitch and no surprise Brighton came back into it once he was subbed off. Newcastle still look very shaky at the back though, a lot of loose balls and Pope doesn't look confident with the ball at his feet.
LostGeordie: A tense and difficult watch. Another dreadful second half - we are supposed to come out at pace but the deliberate slowing of goal-kicks by Pope, perpetually ineffective, was terrible to watch, inviting Brighton's inevitable goal. I'll not comment on Wissa.
Brighton fans
Fran: I thought we had cut out all this silly stuff by giving the ball away in dangerous areas. Verbruggen, again rushing out of his area, and Van Hecke dithering and then slipping. We gifted Newcastle three goals. They were not better than us and we should have won this game. Enjoy the last three games and forget about Europe. If it happens, great - if not, it shows we aren't ready.
David: The Brighton curse of this season strikes again - the inability to beat teams below them in the league. Could have been, should have been almost any score the number of chances created and were not taken. All is not lost - three games to go and we can still get into Europe.
CK: The same old story of attractive approach play was let down by poor delivery in the final third and lack of muscle up top to force the issue. A draw was probably a fairer result.
Jon: If they had been more clinical and defended better, they would have won easily. Verbruggen is a good keeper, but still makes ridiculous errors. Newcastle parked the bus for much of the game.
Newcastle 3-1 Brighton: What Hurzeler saidpublished at 20:13 BST 2 May
20:13 BST 2 May
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Brighton didn't manage 'key moments' - Hurzeler
Brighton manager Fabian Hurzeler speaking to BBC Match of the Day: "We dominated the game except a short period after the two goals. We lost a bit of structure but besides that dominated the game, had the ball and had chances. But the key moments we weren't able to manage well, and that's why we lost.
"Every time you concede a goal you can do something better. We knew they would have physicality on the pitch - height especially at set pieces. The first goal is unlucky decision. I like players who make decisions. If you make decisions and make mistakes then afterwards everyone knows better. I prefer players who take responsibility. All we can do is analyse it and bounce back next weekend.
"The first half we started really well, created chances and had the ball. They were dangerous at set pieces and in transition moments. We knew that, tried to control that, but it's hard to control. At half-time there wasn't much to change. My boys always believe and never give up. We got a goal back and the game could go in a different direction.
"It's not about feeling sorry for ourselves. We will take responsibility, analyse and bounce back."
Did you know?
Brighton and Hove Albion conceded 3+ goals in a Premier League game for the first time since a 3-4 loss to Aston Villa in December.
Bart Verbruggen has made more errors leading to goals (4) than any other player in the Premier League this season, while his 11 since the start of 2023-24 is four more than anyone else.
Analysis: Remarkable run endspublished at 17:48 BST 2 May
17:48 BST 2 May
Ciaran Kelly Football reporter
Image source, Getty Images
Brighton players and staff felt an unfamiliar emotion at full-time. This side had forgotten how to lose, having beaten Chelsea, Liverpool, Sunderland and Burnley in recent weeks and drawn against Tottenham Hotspur.
But manager Fabian Hurzeler will still take a lot of heart from this display.
The Brighton boss handed his players five days off following their impressive 3-0 win against Chelsea last time out.
It was a recognition of how much they had given him and, also, how much trust he had in them to go "all in for the final part of the season" and "give everything for this badge" as he told them when he delivered the news in the dressing room.
They certainly did that at St James' Park and Hurzeler will take a lot of heart from his side's response to going 2-0 down.
They refused to go under and set up a nervy finish at St James' Park after Jack Hinshelwood pulled one back.
Yankuba Minteh even had a glorious opportunity to make it 2-2 against his former club, only to blaze over from close range as Hurzeler dropped to his knees.
Newcastle 3-1 Brighton - send us your thoughtspublished at 16:59 BST 2 May
16:59 BST 2 May
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Newcastle end losing streak with victory over Brighton
Whether you were at the game or following from elsewhere, we want to know what you learned.
Image source, Getty Images
