Boosted by the return of top scorer Joao Pedro - but without Evan Ferguson and Ansu Fati - Albion were ultimately toothless in front of goal on a frustrating night.
Substitute Danny Welbeck had the game's two best chances but failed to convert them as the clock ticked down.
Despite the result, the Brighton boss was very pleased with one of his players in particular. In the post-match press conference, Brighton boss De Zerbi praised his star striker, saying: "Joao Pedro played very well. He makes a difference every time. On the bench, I said 'what a player'.
"It's very tough playing against Brentford. Physical, strong players and it's very tough to win the duel. He won 90 per cent of duals. I'm very happy for him. He's improving in mentality and becoming a top player for us. I would want him to stay with us next season."
Joao Pedro will be a crucial addition back into the Albion squad as they push for a European spot for next season. When asked about what his team will need to do differently in their tough run of final games to achieve their goal he said: "We have to win some big games against big teams. I trust that as when you prepare for games with the right time and not every three days, we are a completely different team."
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