Spaniard Michu scored two late goals as the Swans gained a deserved victory over an Arsenal side devoid of any creativity and sharpness.
Swansea now sit above Arsenal in the table and have moved up to seventh place after the best of week of the club's season thus far.
"It's been a fantastic week for us," Laudrup said.
"We have played three games, and each has been better than the last.
"We have taken seven points from two big teams, Liverpool and Arsenal, and then from the bug surprise team of the season, West Brom.
"Clearly it has been a fantastic week."
The Swans face Norwich at the Liberty Stadium next week knowing that a victory could possibly allow the club to move into the top four.