Albion produced a dominant and high-quality display against a Leeds team who are a handful for anyone in the Premier League.
For the most part, Brighton defended well, played nicely through their energetic midfield and created a host of chances - mainly thanks the brilliance of wide-man Tariq Lamptey.
Where it all went wrong was in front of goal. The recalled Neal Maupay missed two excellent chances and Jakub Moder also wasted two very presentable opportunities and hit the post.
Leo Trossard cracked the woodwork with an excellent first half effort and second half substitute Solly March had two shots very well saved by Leeds keeper Illan Meslier in the dying moments.
The point moves Brighton up to a lofty eighth in the Premier League but it was not enough to prevent a chorus of boos ringing around the Amex Stadium at full time.
Albion head coach Graham Potter was visibly shocked at the final whistle and looked fuming as he addressed the boos during his post match press duties.
"I am a little bit perplexed to the reaction in the crowd at the end because the performance was fantastic against a team that like to dominate possession, like to out-run you - they didn't do that today," Potter said.
"They are entitled to their opinions but I disagree with them completely.
"We are sitting eighth in the Premier League but maybe I need a history lesson on this football club."
So why the frustration and why the boos?
Brighton are now winless in their last eight, including games against Newcastle, Norwich and Leeds, who have all been poor this season.
Albion have scored five goals home and away in their previous eight PL games and the home fans have seen just six goals at the Amex this season.
The performance against Leeds was high class but sticking the ball in the back of the net has been a problem for Graham Potter and his team for a few seasons now.
Playing well without getting the reward is a familiar narrative and that frustration came out from the stands at the end of the Leeds match. It could also have been a lot worse had Tyler Roberts buried his late chance for Leeds.
Albion supporters are frustrated by a lack of cutting edge and are just desperate to see a finishing touch applied to their clever approach play. It's clear Albion need a striker and the boos reflected that.
It wasn't necessarily aimed at Potter or the players but on the overall situation.
Was it justified?
This season, for the first time in the club's history. Albion are a genuinely solid Premier League side. The progress the club has made under Graham Potter has been quite remarkable and the Albion head coach was surprised and hurt by the chorus of boos after Leeds United.
Potter has instilled new belief and they are prepared to go toe to toe with any team in this division. Brighton are currently eighth - above Man United and Leicester - and that is a fine achievement considering the difference in budgets and quality of opposition Albion are up against each week.
Potter rarely complains about injuries - of which there were many last season - and has also introduced numerous youngsters into the team. Another in Jeremy Sarmiento debuted on Saturday.
The style of play is great to watch and he's been able to get the maximum from his senior pros such Lewis Dunk, Shane Duffy and Pascal Gross, while the likes of Leo Trossard, Rob Sanchez, Adam Webster, Tariq Lamptey and Yves Bissouma have all developed nicely under his watch and significantly increased in value.
For all the talk of pretty football, clever tactics, false nines and attacking as a collective, Brighton are a team absolutely crying out for a striker.
Potter fields questions most weeks about cutting edge, silver bullet signings, the final piece in the jigsaw etc etc and the stock answer is always: "I'm happy with the players", or "We can all improve," and "We attack as a collective."
What else can he say? I'm sure he would love a Danny Ings or a Callum Wilson but so far that is not how Brighton operate.
At some stage very soon a striker needs to arrive. So much good work has been carried out on the recruitment over the past few seasons and Potter has shaped this team into a very good looking and interesting outfit.
If the club do not take the final step and back Potter, they may well regret it big time.
Never have Albion had a better team and a better manager and if they don't act, they may never get another opportunity as good as this. Just how far could Potter take this group with a clinical finisher at the sharp end?
It was tough for Potter and the players to hear the boos - especially after they did everything apart from score against Leeds - but lets hope the recruitment team have something up their sleeve for this January.
If not, they could risk losing Potter, and all the good work of the last three seasons.