The Welsh side earned a 1-0 win through Wayne Routledge's second-half strike but could have been behind early if St Gallen's Goran Karanovic had converted a 15th minute spot-kick.
Laudrup admitted his side had played poorly but was ecstatic they had snatched the three points and praised his squad for the result.
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|18/1||Swansea are 18/1 with Bet365 to beat Southampton 2-0 on Sunday
"Normally, to win, we always have to play well. I am pleased with the win but it was probably not one of our best games.
"In Europe, it's tight and always difficult, and I think St Gallen showed today that they have a good squad."
Swansea started their Europa League campaign with a stunning 3-0 win at Valencia and Laudrup believes victory over St Gallen has put his team in the driving seat ahead of their next match against Russia's Kuban Krasnodar.
"We are in a really good position because Valencia won away and St Gallen won their first game at home," he added.
"So now, after two games, we have six [points], 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.
"You need maybe 10 points [to qualify for the knockout stages of the Europa League], 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."