Wayne Routledge got the only goal of the game six minutes into the second half, tapping in at the far post.
Swansea were a long way short of the form they showed in humbling Valencia at the Mestalla in their first group game, and the visitors would have taken something from the game had striker Goran Karanovic converted a first-half penalty.
The game was hardly helped by the inconsistent and fussy refereeing of Duarte Gomes, but Swansea can now head into the home game with Kuban Krasnodar later this month knowing a win would put them a long way towards a place in the last-32.
"I am pleased with the win," said Laudrup. "It was probably not one of our best games but in Europe games are tight and it is always difficult.
"The most positive thing is I don't remember the last time we managed to win when not playing well. Normally we have to play well to win, but tonight we didn't, although we had good moments.
"We had more chances then them, but if they had scored their penalty and another good chance they had it could have been different.
"But we have had games where we have failed to take our chances.
"I have said in recent weeks we have played well and not taken our chances. Maybe they deserved more but that's football."
Laudrup had few complaints with the penalty awarded against Dwight Tiendalli, but admitted to being frustrated by the eight-and-a-half minute spell in the first half where Swansea were down to 10 men with Michu receiving treatment.
The Spaniard suffered a cut after being hit in the face by Stephane Besle's boot, and Swansea were furious referee Gomes did not stop play as the forward was left sprawled on the turf.
Michu got to his feet with blood streaming from a cut and a farce developed as efforts to stem the flow, including vaseline, bandages and a change of shirt, all failed.
He was then prevented from returning as blood seeped onto his change shirt, before a numberless jersey was finally deemed up to standard and he wandered back on.
At half-time a member of Swansea's staff was sent to the club shop to retrieve a shirt with his name and number on the back, but even that was changed for a fifth of the night during the closing stages.
"We did not know how bad it was, because he was on the other side of the field," said Laudrup.
"We said he would come back on, but we were eight minutes with 10 men.
"Fortunately nothing happened, it was not bad for him and we did not concede.
"There was a little bit of blood, so he changed to one with no number."
When asked about the dash to the club shop for a new shirt, Laudrup joked: "Wasn't it closed?
"He had some stitches at half-time. I don't know how many."
But the Dane acknowledged his side are now very well placed in the group.
He continued: "We are in a fantastic position, Valencia won away in Russia so we have six points, and there are two teams on three points and they play each other next time.
"If we could win the next game it would be a really good position."
St Gallen boss Jeff Saibene was disappointed his side had come away with nothing, and also confirmed when Karanovic was substituted with concussion at half-time - following a collision with goalkeeper Gerhard Tremmel, he had no memory of his penalty miss.
Saibene said: "I think we deserved a point, we had clear chances and kept them at bay in the first half so it is a bitter defeat.
"With the penalty, we are used to that as this is the fifth penalty we have missed in two years."
He added: "Karanovic has seriously injured his head. I don't know if he needs to go to hospital. He got a real knock on the head but the doctor has to look at him first. He is still being treated.
"But he did not remember he had missed the penalty, maybe he won't want to see it again."