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:
1. Toffees still keen on Diaz
Everton are believed to still have an interest in signing Porto striker Luis Diaz, despite failing to sign the Colombia international. He's likely to cost around £42m, after dazzling in the Portuguese top tier and the Champions League so far this season. (Sport Witness) Photo: Clive Brunskill
2. Duo jostle for Insigne
Newcastle United and West Ham have both been alerted to the possibility of signing Napoli skipper Lorenzo Insigne, who could leave Napoli next year after failing to reach an agreement over a new contract. He played a key role for Italy in their Euro 2020 winning campaign. (Calciomercato) Photo: Claudio Villa
3. Saints keen on Freckleton
Southampton are said to be among a number of clubs interested in signing Bristol Rovers defender Miguel Freckleton. The 18-year-old is believed to have spent time on trial with the Saints, as well as Sheffield United and Hull City. (Bristol Post) Photo: Harry Trump
4. Gerrard readies Gers raid
Aston Villa boss Steven Gerrard is believe to be plotting to raid his former club for teenage ace Leon King, who could be available for just £200k. The 17-year-old is also believed to be on the respective radars of Man Utd, Newcastle and Leicester City. (Birmingham Mail) Photo: Ian MacNicol