The Swans went into Sunday's Premier League clash at the Hawthorns pointless after succumbing to Manchester United and Tottenham in their opening two games.
But Laudrup was pleased to see his side get off the mark, following a tough opening to the new campaign as goals from Ben Davies and Pablo Hernandez gave them a 2-0 triumph.
"Things to be pleased for today, first of all the win, first three points after two very difficult games against Manchester United and Tottenham - a very good performance, an away win and clean sheet so it was a complete day," Laudrup told Sky Sports.
Laudrup admits that taking on West Brom was a different proposition to their game at Tottenham last weekend.
"You have to take into account the opponent, we dominated against a team who I call from our league, us and West Brom are in the same boat but Tottenham they play for other things and you have to admit they are a very strong side."
Speaking ahead of transfer deadline day, he confirmed he was hoping to bring another striker into the club.
"I've been asked about a lot of players and I've always said we want one more striker with different characteristics to Wilfried Bony and Michu," he said.
"We will add one tomorrow. We've had five, six, seven players linked and one will join, but not more than one.
"We have to go into the last day (of the window) having not done everything which is not ideal because it will be a crazy day, but hopefully we'll finish in time.
"I don't want to go into details but let's say we hope to finish it as quickly as possible."