It was Norwich's fifth straight league defeat and Daniel Farke's side have not scored a goal since the season restarted last month after the COVID-19 hiatus.
They stayed at the foot of the standings with 21 points -- seven behind 17th-placed Watford -- and relegation from the top flight for the third time in seven seasons looks increasingly likely with five games left.
"It was more or less our last chance to get back in the mix and we are disappointed. It was more like the performance we ask for," Farke told the BBC.
"The story of our game was the story of our season, we didn't find the cutting edge and we then make a big mistake. After a few losses, we don't have the right to make any fighting messages or to make any unrealistic claims."
Brighton took the lead midway through the first half from a sharp counter-attack in which Aaron Mooy found Trossard in the box and the Belgian calmly slotted the ball into the bottom corner with a first-time shot past goalkeeper Tim Krul.
Norwich stayed bottom of the standings with 21 points, seven behind 17th-placed Watford, while Brighton remained 15th.
Brighton have now picked up seven points in their last four games to boost their chances of staying up.
"It's one of those days when the result is the most important thing," Brighton manager Graham Potter said. "To get three points and a clean sheet you need a little luck, and we had it at the end with the post.
"We've got five more games to go and we're still fighting for the points... 36 (points) is a decent number, though we need more."