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:
5. Race heats up for Aribo
Crystal Palace, Watford and Brentford have all been credited with an interest in Rangers midfielder Joe Aribo. The 25-year-old made 31 appearances in the side's title-winning campaign last season, and has 18 months left on his current contract. (Daily Mail) Photo: Ian MacNicol
6. Potter could be considered for Man Utd job
Manchester United could make a move for Roberto Mancini as their next manager, while Brighton's Graham Potter and Sporting CP's Ruben Amorim could be left field options the club could pursue instead. (Telegraph) Photo: Alex Pantling
7. Leeds linked with Ferreira
Reports from Brazil have claimed Leeds United are keeping tabs on Palmeiras boss Abel Ferreira - who has a whopping £25m release clause - should Marcelo Bielsa leave at the end of his current deal. However, the report notes that the Whites' preferred option is to hang onto their current manager. (Sport Witness) Photo: JUAN MABROMATA
8. Nketiah turns down new deal
Arsenal striker Eddie Nketiah is believed to have turned down a contract extension, meaning he could join a foreign club for nothing in January. The ex-Leeds loanee had been recently linked with a return to Elland Road, but the move looks to be unlikely. (Sky Sports) Photo: Julian Finney