Martha Thomas gave West Ham the lead with a close-range finish on 24 minutes before Kenza Dali fired home a second from the penalty spot.
An excellent strike from Alisha Lehmann made it three for the Hammers and sealed a second win from their first four matches in the Women's Super League.
Powell's team, who have two draws and a defeat so far this campaign, reduced the deficit in injury-time thanks to Megan Connolly's effort following a corner.
The Seagulls almost took the lead early on as Aileen Whelan's lob hit the post but West Ham were the better team throughout and controlled the majority of the match.
Powell said, “I thought we started quite well, but we capitulated a bit after they scored and found it difficult to get our groove back.
“Credit to West Ham as they played on the front foot and it was a bit tetchy at times from both teams. I was pleased with the first 25 minutes, but we struggled a bit from that point, and it wasn’t until we scored late on that we managed to liven up a bit."
Goalkeeper Megan Walsh’s was Brighton's best player and made a couple of fine saves to keep the scoreline respectable.
“She is a huge addition for us and pulled off a couple of good saves," Powell added. "She can only get better in my opinion, but it’s got to go through a lot of players before it gets to her. Those players in front of her have got to do better.
“We had a long chat in the dressing room after the game to understand how we’ll put this right going forward. We need to understand why we played within ourselves and became withdrawn after their opening goal. It was a very helpful discussion, as it was about doing the basics well and understanding that the league is very unforgiving.
“We stressed that we can’t cut any corners, and we’ll have to dust ourselves down and go again.”
Brighton are next in action on Sunday, October 20 in the Continental League Cup as they welcome Bristol City to the People's Pension Stadium.
ALBION: Walsh; Lundorf, Williams, Kerkdijk, Gibbons; Simpkins (Le Tissier 46), Bowman, Le Garrec; Brazil (Connolly 74), Umotong (Green 59), A. Whelan.
SUBS NOT USED: Harris (GK), Barton, Hack, Natkiel.