I agree with you regarding Brighton's volatility this season, and that 4-0 loss makes Europa League advancement unlikely. Thinking about the mountain they must climb against Roma in the second leg is discouraging. The unpredictable character of football must be remembered. Brighton's performance against smaller teams has been inconsistent, so its a long shot. This sport is beautiful because of its unpredictability. Who knows, Brighton could be the next miracle?
You're right about English teams outside the big 6 performing poorly abroad. Squad depth and international focus differ from the domestic league. However, every encounter is a chance for Brighton to prove themselves. Lets be optimistic. Even if they dont advance, this Europa League experience will help the club improve in future European events.
Brighton's performance in competitions other than the domestic league is indeed poor because Brighton does not have more experience than Roma, who appeared strong in the European League, so Roma is confident enough to compete here. However, initially I also favored English clubs because usually English clubs are stronger than any club, but it turns out that this has not been fully proven, many English clubs have been disappointing in big competitions this season, such as Newcastle and Manchester United, who failed to qualify for the Champions League and I think Brighton too will experience something similar, their struggle only reached this round.