Everton were booed off after their dismal run extended to just one win in their last 12 league games.
Everton sit eight points above the relegation zone and Benitez will know results must improve quickly if he is to avoid increased talk of the sack.
Brighton made the perfect start with a third-minute opener as Joel Veltman’s cross was nodded on by Neal Maupay for Alexis Mac Allister to net with a clinical volley.
Dan Burn doubled Albion’s lead with a header after Everton were caught flat-footed by Mac Allister’s 21st-minute corner.
Just when Benitez thought things could not get any worse, Dominic Calvert-Lewin blazed a 25th-minute penalty high over the bar.
The spot-kick was awarded after VAR recommended referee John Brooks took another look at Enock Mwepu’s challenge on Anthony Gordon.
Gordon gave Everton hope when his shot deflected in off Adam Lallana after 53 minutes.
Mac Allister lashed home from 25 yards with 20 minutes to go before Gordon’s close-range finish reduced the deficit again six minutes later.
Benitez speaks after the game
“I don’t like to make excuses. The goals we conceded is the lack of focus in the first minute and then after you play under pressure. You could see the reaction was there but it is not enough because you still make mistakes,” Benitez said.
“I’m concerned that we have to improve, especially in defence. The team pushes and works hard and tries but we are lacking a little quality in the decisions.”
Leeds boosted their survival bid with a 3-1 win against fellow strugglers Burnley at Elland Road.
Marcelo Bielsa’s men had lost their last three games, conceding 14 goals in the process.
Jack Harrison fired Leeds ahead on 39 minutes and Maxwel Cornet equalised with a 54th-minute free-kick.
Burnley’s Matt Lowton was struck in the face by a plastic bottle thrown from the crowd as Sean Dyche’s players celebrated Cornet’s goal.
Stuart Dallas put Leeds in front from 20 yards in the 77th minute and Daniel James wrapped up the points in stoppage time.
Leeds are now eight points clear of third-bottom Burnley in the fight to avoid relegation.
Brentford came from behind to beat Aston Villa 2-1 thanks to Mads Roerslev’s close-range finish in the 83rd minute.