Klopp admits his Liverpool players are 'low on confidence' after draw
Liverpool have won only won two of their first seven league games of the season to already fall 11 points behind leaders Arsenal, who they face at the Emirates next weekend.
Klopp's men were starring down the barrel of a first league defeat in front of fans at Anfield since 2017 when the Belgian scored twice inside the first 17 minutes.
The Reds looked to have turned the game around when Roberto Firmino (30) struck twice either side of half-time before Adam Webster's own goal put the home side in front.
But in Roberto De Zerbi's first game as Brighton boss, the Seagulls got the reward their performance deserved when Trossard (27) fired in at the back post seven minutes from time.
"The confidence level is not extraordinarily high," said Klopp, whose side are suffering a hangover after narrowly missing out on winning a quadruple of trophies last season.
"We should defend all three goals better. We have to fight through this, the boys can play much better.
"My job is to create a situation where we can play much better."
A point leaves Liverpool down in ninth, while Brighton remain in fourth.
De Zerbi's debut after succeeding new Chelsea boss Graham Potter lived up to the hype as the Italian's brand of intricate passing out from the back cut Liverpool to shreds in the early stages.
"Potter deserves some credit because he has left to me a great team," said De Zerbi.
"I have tried to not make any damage and add my idea on top."
Klopp spoke out at length in defence of Trent Alexander-Arnold (23) after he was overlooked by England manager Gareth Southgate during the international break.
But critics of Alexander-Arnold's defending were given more ammunition after just four minutes when he was turned by Trossard and the Belgian fired into the far corner.
A nightmare opening 20 minutes for the hosts could have been much worse but for two big saves from Alisson Becker.
Danny Welbeck placed his header from close range too close to the Brazilian, who then produced a brilliant stop as he flew off his line to deny Trossard.
'Horrible' viewing for Klopp
However, Liverpool were not so lucky when they passed up a third big chance after the opener as Brighton again worked an opening down the side of Alexander-Arnold and Trossard's strike had too much power for Alisson.
"It was horrible to watch how many times their offensive players could turn between the lines," added Klopp.
"Usually we adapt quicker. Before we adapted, we were 2-0 down."
Klopp summoned Virgil van Dijk to the touchline after the second goal in a bid to restore some order and the Reds did get a foothold before the break.
Firmino's fourth goal of the season was initially ruled out for offside as he dinked into an unguarded net after Mohamed Salah knocked the ball past Robert Sanchez.
A VAR review came to Liverpool's rescue, though, to halve the arrears.
Klopp had surprisingly left Luis Diaz, Diogo Jota and Darwin Nunez on the bench from the start, but Diaz replaced Fabio Carvalho at the start of the second half.
The Colombian made a quick impact as he charged at the Brighton defence and laid the ball across for Firmino, who cut inside Lewis Dunk and coolly found the far corner.
Brighton orchestrated their own downfall for Liverpool's third as Sanchez punched the ball into his own net off the unfortunate Webster.
But true to De Zerbi's reputation as an attack-minded coach, the visitors never stopped piling men forward and finally took one of their chances when Trossard turned home Kaoru Mitoma's cross.
