Despite being away from home, the Seagulls dominated much of the game, and will feel the result was a fair reflection of their efforts.
Speaking after the game, Brighton boss Graham Potter gave an injury update on teenager Jeremy Sarmiento, who was substituted off with an injury after just 13 minutes.
Potter said: “It's a real blow on his first start. I saw him briefly and obviously he's disappointed. I'm not sure how it happened I haven't spoken to him on that yet. It's his hamstring so we don't yet know the full extent of it until it settles down.
“Obviously really disappointing for him and the team. He and the two Adams (Webster and Lallana) both suffered today and they and Jeremy will certainly not be involved against Southampton.
“It was a bit of muscle bingo there but we have a group and we have a squad and we have to adapt but clearly it is not the best."
Potter added: “It was an eventful game. The character of the team is amazing and the spirit is amazing they keep pushing and pushing. We were the ones trying to create. West Ham are really dangerous on the break but we showed good control.
“It is not easy to create because they defend so well. It was a great finish and it just goes to show one day you are the villain and the next you are the hero."
Next up, the Seagulls travel to take on Southampton at St Mary's on Saturday afternoon.
Here is our rundown of the latest news and updates from the Premier League, as the build-up to this weekend's eagerly-anticipated action begins:
9. Clarets step up chase for Fulgini
Burnley are believed to be front-runners to sign SCO Angers midfielder Angelo Fulgini, ahead of the likes of Brighton, Lyon and Fulham. The Clarets are said to be willing to spend around £12m on the Ligue 1 ace. (Foot Mercato) Photo: FRANCK FIFE
10. Red Devils eye Werner
Reports from Germany have suggested that Man Utd could target Chelsea flop Timo Werner in January, as the Red Devils look to improve their squad. He played under the Red Devils' interim boss Ralph Rangnick during his time at RB Leipzig. (talkSPORT) Photo: BEN STANSALL