Roberto De Zerbi had guided the Seagulls through to the Europa League last-16 with a four-match winning run in the competition, but first-half goals by Paulo Dybala and Romelu Lukaku put the visitors on the ropes in Rome.
Worse was to follow after the break with Gianluca Mancini and Bryan Cristante able to score in quick succession to essentially kill the tie.
The Premier League outfit did have their chances with Danny Welbeck denied on several occasions, but injury-hit Brighton need a miracle to overturn a four-goal deficit in next week’s second leg.
De Zerbi and opposite number Daniele De Rossi exchanged a number of pleasantries on Wednesday with the Seagulls boss labelled a “genius”, but it was a different story out in the streets of the Italian capital with two Brighton fans stabbed the day before the match.