West Brom came into the game sitting third in the league and riding a four-game winning streak but were torn apart by Swansea, who were 3-0 up after 40 minutes through Michu and a Wayne Routledge double.
The Baggies pulled one back through Romelu Lukaku in first-half added time, and gave a better account of themselves in the second half, but Laudrup said Swansea had been different class.
"We were outstanding in the first half. It's not often that a manager can just sit back and enjoy his team playing," he told the club's official website.
"We showed what we can do when we are at our best, but it is always difficult to do that for the full 90 minutes.
"The game also showed that little things can change games, because when they scored, their game immediately altered a little. But I don't think West Brom created any great chances in the second half, and it was a pleasure to see my team perform like they did."
"It will be a completely different game," said former Danish international Laudrup, who took the reins of the Welsh club in June. "Arsenal are a very good side, with some great players who like to play on the ball.
"But we go there with no pressure and we can surprise people. We have got four points this week which has been a very good return for us."
His West Brom counterpart, Steve Clarke, was shellshocked at Swansea's first-half onslaught and admitted the Baggies had been caught cold.
"We started so slowly it was incredible. You wouldn't have believed we could start so slowly," said the Scot.
"We knew they would cause us problems but we didn't expect them to cause us so many problems so early in the game. Swansea got the quick start and got in front of us and we left ourselves too much to do."
"It was very unexpected," he added. "We've had a really good season, we've played really well and we've had four wins in a row.
"The team was good and we went into the game confident, we went with more or less the same players and the same system but it's football and it happens."
