Andy Carroll netted the winner for the Hammers 13 minutes from time with just his second goal in claret and blue.
Swansea, for all their pretty football, only sprung to life after Carroll's goal and top scorer Michu had a rare off-day playing on his own up front.
Wayne Routledge gave Matt Taylor a torrid time down the right flank but Swansea's final product was poor and they rarely tested Hammers goalkeeper Jussi Jaaskelainen.
But Laudrup said: "We dominated quite well in the first half.
"They gave us more or less what we expected. We had the ball more but they played direct and we know how good Carroll is in the air. Inside the box he's very dangerous.
"We could have won 1-0 or it could have been 1-1. After they scored we came back, had a few chances to equalise, but we just have to accept it.
"We're very difficult to beat. Nobody likes to lose. We're not used to losing after the last seven weeks."
- Sports & Recreation
- Andy Carroll
- Wayne Routledge