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Diego Gomez’s thunderbolt volley opened the scoring 15 minutes in for the Seagulls, before Thiago was sent off for striking Chema Andres in the face after a VAR review.
Pascal Gross doubled Brighton’s lead from the penalty spot after Keane Lewis-Potter dragged Luka Vuskovic to the ground, and 10-man Brentford were unable to breach their defences in the second half.
Andrews said: “We’ve lost two games this season and both have been when a man has been sent off. We look in the mirror first and how we can do things better.
“I do think our players need more protection. On both of those occasions that our player has been sent off, it’s the opposition players that have antagonised the situation. We need to do better but it’s a sad indictment of where the game’s going at times.
“I’m very unhappy with a lot of players’ reaction within the current game. How they go down, how they hold their faces. I think this may become a gameplan within the game. We’re not that type of team. We’re a very honest team and we endeavour to push the limits hard, to play with an edge.”
The result meant the Bees were leapfrogged by Everton and Bournemouth, leaving them eighth in the Premier League, while Brighton continued their electric start to the season and sit second after 10 games played.
Andrews added: “A lot of teams would capitulate against Brighton with 10 men. We’ve seen this season the level of chances they can create and the goals they can score.
“It’s testament to us as a group that we dug in and they didn’t score a goal in the second half. We tried to play our way out and force set pieces, going to a back four. But it’s very difficult against that team.
“The grit, resilience, and spirit of the group was on full show in the second half and I was proud of us.”
Brentford face Everton next on the first Monday after the international break.