Despite picking up a second victory in the competition, the Dane admits his side did not play well but feels they are now in the driving seat to qualify for the knockout stages
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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"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."