In a turgid game of few clear chances the Hammers' dead-ball threat troubled their hosts all afternoon, with Angel Rangel hooking a long Razvan Rat free-kick off the line, while Guy Demel and Kevin Nolan also spurned sights of goal.
Jussi Jaaskelainen made two point-blank stops to deny Chico Flores and Wilfried Bony at the other end, but the hosts were most aggrieved referee Phil Dowd's decision to turn down a stoppage-time appeal for handball against Joe Cole.
The West Ham substitute had his arm raised as he leapt to block a Nathan Dyer cross, and Laudrup had no doubt his side should have had a spot-kick.
"I think we deserved more, but on the other hand Jaaskelainen had made two or three fantastic saves, so you can't do anything about that," he said.
"There was a lot of emotion in the end which was about the penalty which was not given.
"I know I always say that a referee or a linesman only has one second, but I mean it is so clear when you have your arm up like that.
"If you have your arm down you can talk about hand to ball or ball to hand, but when you have your arm up there and it hits you, normally nine out of 10 times it is a penalty.
"Of course when you have a case like this in the 91st minute, there are a lot of emotions,
"But we know that the relationship between Swansea and penalties is not the best, even if we got one last weekend against Sunderland after 50-something (56) games.
"Not to be funny, but maybe the fans and everybody here should buy a t-shirt to say that 'I was there when Swansea got a penalty'.
"But it is done and it's gone and we can't turn back. It's just that when you have a situation like this, we have had penalties against us for things like that.
"It is a reflex because no one wants the ball in his hand but the rules are that if you move your arm and it touches, it is a penalty. But not today, maybe another day."
West Ham boss Sam Allardyce, who did not attend his post-match press conference, again opted to start with a side containing no recognised striker, and their 4-6-0 formation stymied Swansea's passing game, while they carried a potent threat from set-pieces at the other end.
But Laudrup was content with his side's display as they look forward to next Sunday's derby with local rivals Cardiff.
"I knew it would be very difficult as they enjoyed huge success playing like this against Tottenham, winning 3-0," said Laudrup.
"We knew they would play without a striker and with six in midfield and it is difficult.
"You also know they are so good at set-pieces and we had some problems when they had four or five consecutively in the first half.
"We don't have the tallest guys but in the second half, despite not being at our best, we controlled it.
"They sat very deep and Jaaskelainen was man of the match for me.
"I always want to win but we move up the table and this is okay."
- Sports & Recreation
- Angel Rangel
- Wilfried Bony
- Chico Flores