Wayne Routledge scored the only goal of the Group A encounter seven minutes into the second half after Swansea keeper Gerhard Tremmel had saved a first-half penalty.
Swansea manager Laudrup acknowledged it was not one of his team's better performances and was satisfied to make it two wins from two games in the group phase.
"I'm pleased with the win," said Laudrup. "But it was probably not one of our best games.
"In Europe, it's tight. It's always difficult, and I think St Gallen showed today that they have a good squad.
"They confirmed what we have been analysing - that they are a very hard working team; they play 90 minutes with high rhythm and I think they did very well.
"For me, the most positive thing - other than the result - is that I don't remember the last time we won without playing well. Normally, to win, we always have to play well.
"We created the five or six chances that we always do, but without playing well.
"They probably deserved a little more, but 'deserve' and 'justice', in football, doesn't exist."
He added: "We are in a really good position because Valencia won away, and St Gallen won their first game at home. So now, after two games, we have six, with two teams on three who have to play each other.
"If we can win the next game against Kuban, we will be in a really, really good position.
"From my experience in the group stage, you have to win your home games. You need maybe ten points, so if we win the next game, we will need one point from three games, but if we can be top of the group, even better."