Neal Maupay's header condemned interim head coach Ljungberg to a 2-1 defeat in his first home game in charge.
The Gunners have now gone nine matches without a victory, their worst run in over 42 years, with Ljungberg unable to oversee an immediate upturn in fortunes following Unai Emery's sacking last week.
"It's tough, they looked low on confidence in the first half," said Ljungberg. "We need to dig out a win to get some confidence. It's obvious the nerves in the crowd affect the players.
"They are human beings, they want to do well and they feel pressure. But we need a win and we showed in the second half we can get one."
Brighton were dominant against a lacklustre home outfit and took a deserved lead from a corner, Adam Webster sweeping the ball home from Dan Burn's knock-down and Aaron Connolly's touch into his path.
The Gunners should have drawn level before half-time after Pierre-Emerick Aubameyang stood up an inviting cross, but Joe Willock could only head it at straight at goalkeeper Mat Ryan.
Ljungberg threw on record signing Nicolas Pepe at the break and Arsenal immediately looked brighter.
It took them four minutes to equalise, as Alexandre Lacazette's flicked header from Mesut Ozil's corner looped up and in off the far post.
David Luiz had the ball in the net after an hour but he was clearly offside when he met Ozil's free-kick and VAR chalked off the goal.
Instead Brighton secured a notable win when Aaron Mooy was given too much space down the left to swing in a cross and Maupay got ahead of Luiz to glance a header home.
Arsenal almost snatched a point but Ryan kept out a late header from substitute Gabriel Martinelli.
The Gunners, who are down in 10th place in the table with 10 points between themselves and the top four, next travel to West Ham on Monday.