Eden Hazard scored the only goal of the Premier League encounter in the 29th minute at Stamford Bridge - his effort from just inside the penalty area sneaking under Swansea goalkeeper Gerhard Tremmel.
The goal came in a first half that saw Chelsea completely dominate, but Swansea were more competitive after the break as Chelsea failed to finish them off.
And Laudrup hailed his players for their approach to the match.
"When you play against teams like this you will have different parts of the game where you have to suffer a bit," he said. "We had 15-20 minutes in the first half where were under pressure and we had to defend too deep.
"I thought the intention from Chelsea (after the goal) would be to try to finish the game off.
"But i think we came okay in the game again and the fact that we were in there until the last second was positive."
The Dane also insisted there was no shame in losing narrowly to a team of Chelsea's calibre.
"When you play teams like that, they have those quality players that just make the difference," he continued.
"Hazard, Oscar, (Juan) Mata - we're talking top top international level.
"There's a reason why these players play in certain teams."
Swansea will bid to end a four-game winless streak in the Premier League and avoid a third defeat in a row when Laudrup's men travel to Aston Villa on Saturday.
